in honor of me being sick for like the 2nd? 3rd consecutive week? and not seeing much notable progress, i'm going to rate how good each main TAU character would be at taking care of you during illness:
TAU!swap has all of a sans' social intelligence and all of a papyrus' energy. he could be a nurse. he could be your weird but loving mom. he's researching shit, he's bringing you medicine, making you soup. he's the picture of confidence; he has this shit under control, you can rest easy. ...this situation would be the most ideal if you knew and liked him personally, because i can't imagine something more miserable than being sick and vulnerable with someone who's trying really hard to help you but you're just cognitive enough to feel the awkwardness.
(he would have probably insisted on taking me to the hospital by day 5 of sickness, but alas, he's not here to pay my bills or do my chores.)
killer's approach would be very clinical and detached but effective, like a robot belatedly reprogrammed to be a nurse. he doesn't know what's wrong with you but he has books that do, and he can follow instructions like a champ. he'd probably try to distract you, but not very well; bedside manner is where he'd fall apart. he doesn't mean bad, he's just not good at taking care of emotions, no matter whose they are. you're sad? you're scared? you feel bad? well, look, he already did what he was told to do to fix it and you complained when he started joking, so he doesn't know what to do. TLDR; you'll recover, but the relationship won't really have gone anywhere for it.
if he had a reason to want you alive, i think he'd be one of the best at doing it. again, bedside manner is lacking; he's kind of a manbaby and an incel, so he's not in the top 5 people i'd want watching over me in a time of pain and vulnerability. however, he's also ridiculously fucking smart, and out of the entirety of TAU's cast probably knows best how a human works. no need to waste time at a hospital — he can read your code and find out what's wrong with you, and after that, humans have a medicine specialized for just about anything.
...but also if you have any fluids coming out of you anywhere this all falls apart; he'll squeal and whine and refuse to enter the room. and even if there's no grossness you'll still have to deal with him watching his novellas way too loudly and screaming at the "tv" because he forgot you were there. you'd live, but... you wouldn't feel very rested.
he doesn't really know what he's doing, but he's arguably got the best intentions, and he knows enough about human anatomy to bullshit it surprisingly well. you probably wouldn't even realize he had no idea what was wrong with you or if he was doing the right thing to help; he just quietly assesses your temperature, googles what temperature a human is supposed to be, and then tries to get you to rest. better yet: you could puke directly on him and he wouldn't care. he's woken up from bad episodes before covered in his own vomit, not to mention the piss and shit of humans he's killed. you think you can faze him?
...the others might be bothered, though, because dust is notoriously difficult to get to do anything that requires him to undress even a tiny bit, including bathe. so maybe try to aim at the bowl he brings you?
he has some experience with humans, but not much with sickness owing to his dad's hardon for "perfection", so his approach would be like someone trying to follow the lines of a storybook by distant memory; awkwardly tucking you in, going to buy canned chicken noodle soup (it has to be that kind, that's what humans eat when they're sick, there must be a reason why). if you're a type of sick that doesn't match up with that treatment though he'll start visibly panicking and that will probably make you feel worse. don't worry, he'll — he'll find someone that knows what to do. just — don't move.
normally i'd say that abaddon has a very high-functioning case of ASPD, but this is definitely their limit. they're a huge germophobe, and i struggle to think of a relationship you could have with them or a favor they could owe you that would be enough to overcome that without any empathy acting as a guardrail. they might try, but less in the "swallowing their own discomfort for you" kind of way and more in the "putting a cold, too-wet towel on your forehead from across the room using a broom handle because they don't want anyone to be able to say they didn't do anything" kind of way. if any undue fluid comes out of you (or even if you just sneeze or fart in their general vicinity) they're tapping out and going to get someone else, no matter their relationship with you. they also just don't know how to take care of anything while it's sick, themself included — they're almost always at least a little sick, and they usually just brute force it until the symptoms get better or they wake up somewhere unfamiliar.
he wants to help, but he doesn't know how. he tries feeding from you (he doesn't know that's how his powers work) to make you happy, and it works for a little bit, but then you crash super hard afterwords and for reasons unknown to him you seem to get sicker. how often do humans need to eat? (you said you're not hungry; surely you know best.) how often do humans need to sleep? (16 hours is normal, right?) he's so, so so anxious that it will leak over onto you even if you're practically in a coma. i get stress cramps just thinking about all the hand-wringing and desperate telephone calls he'd be doing. forget being a decent nurse; he wouldn't even be a good babysitter. he could kill a goddamn sidewalk weed just from making it nervous.
nightmare unfortunately also knows next to nothing about how humans work, only he has no excuse. (the reason is just disinterest; abaddon's been the only exception, but they're self-sufficient enough that he hasn't felt the need to learn.) he also has basically no idea how to help, except he thankfully has enough sense to refrain from feeding from you. (though he would entertain the idea — he feeds from misery, what if some of the sickness came with it? hmm...)
on the bright side, he's at least aware enough of his own inexperience that he'd call someone else before you ended up hospitalized or dead.
he's good at killing humans, not keeping them alive. he only cooks for the team to have control over the food; his meals are utilitarian and harshly proportioned, and only as tasty as they needed to get for the others to agree to let him cook. he would be against the idea of you getting more food in the first place, sickness or not, because it would throw off his system. i love horror, but he's really not the guy for this.
(to be fair, though, the sudden spike in brusqueness and emotional distance would be because seeing you sick triggered him — some part of him thinks you're going to die and is not only trying to prepare, but trying to protect the others by not letting you use resources you'll ultimately "waste". still doesn't excuse the behavior, but yanno.)
oh man, he was supposed to take care of someone?