Ilya and Shane are both equally terribly when they get sick, just in different ways.
Shane is in full on denial when he gets a cold, like he could be coughing his lungs out and be like: This is fine🙂 (the frog smile is important), internally repeating "mind over body, mind over body". He would probably play a game while having pneumonia if his enemy no. 1 (the team doctor) wouldn't harass him about "having to cure it firstly". Shane is extremely good at hiding that he gets sick and if it still gets out, he tries to downplay it as much as possible to get back on the ice as quick as possible, while simultaneously being an incredibly difficult patient who would get irritating and snappy at anyone would try to comfort and pamper him. Shane hates when everybody seems to know better than him what he needs or what to decide over his head. Even when it's just someone offering an additonal blanket, or asking if he is alright - Shane really doesn't take that well. And this probably something he did already from a young age on, like he learned how important it is to be seen as strong, consistent, reliable, always in control of his mind and his body. Shane Hollander has got way better things to do than being sick, and also people counted on him being in top form all the time, so no thank you, he won't 'go back to bed and rest'.
It takes a good amount of time and healing for him to allow himself to acknowledge his vulnerability and accept this emporary weakness and trusts Ilya to take care of him. It is such a milestone for Shane when someday, he wakes up in the morning with a sore throat and instead of ignoring it, he immediately tells Ilya and quitely asks him if he could make him a hot cup if tea with honey. Because he knows Ilya doesn't see him as fragile, he only takes over the control that Shane hands him over willingly. For Shane, Ilya is the only other person who knows what Shane needs, sometimes even better than himself.
(But still, the only thing Ilya is not allowed to is getting in between Shane and hockey, that man would skate with a nasty fever and there is nothing even Ilya can do about but take properly care of Shane afterwards).
Ilya is the worst manchild ever when he is sick. The slightest bit of a runny nose and he is whining as if there is no tomorrow, claiming he is too weak to even lift a finger. Shane is busy running around the house to go fetch a glass of water, open the windows, close the windows, take Ilya's temperature, change the tv channel, read to Ilya, open the windows again, snuggle Ilya, make him soup, close the window, read to Ilya, rub his chest with balm (a task Shane is very devoted to). When Ilya gets a cough he proclaims he is short of dying, like "No really Shanya, for real this time, I feel my soul living my body already, goodbye beautiful world, humankind will lose greatest hockey player but I shall play among the angels soon, Solnyshko, promise me to never get married again, okey?' Shane rolls his eyes at him and calls him an asshole and also tells him that this is because of those damned cigarettes, and Ilya pouts at him until Shane continues stroking his hair. But that near-death experience doesn't stop Ilya from going to hockey practice two hours later. And the thing is, Shane knows that this is an act but he doesn't really mind. He loves taking care of Ilya and turn into Supreme Husband 3000 mode. Shane adores his dramatic menace, that's his baby!! He wants to take care of Ilya, knowing that noone else did since Ilya was a little child. So yes, Ilya is allowed to revel in all the attention and love, getting spoiled to no end. And it's not like it wouldn't be in Shane's interest too when Ilya is extra clingy and demands even more cuddles than usual. The cuddling just finds an abrupt end when Ilya is miraculously cured just in time for hockey tho (and afterwards needs some extra attention to get better, of course).
Only problem is, that if one of them gets sick the other one follows suit like two days later max. There is no way either one of them would withstand the torture of not kissing each other, even in their most yukky, snotty states.
They are both extremely stubborn tho and of course compete in the world's best husband contest trying to take care of the other while Ilya and Shane both feeling like shit. It's like rhe world's slowest race as they are dizzy with a cold and tumble towards the kitchen to make the other one a hot water bottle, sniffling and begging each other to just stay in bed, 'I got this' while neither of them got this.