i think it's helpful to work on redirecting that shame into gratefulness.
someone telling you no or that you've hurt them is a gift. it is a very brave thing to say, and it helps you know what you need to do to fix things or prevent future harm.
even if you can't stop having a breakdown, first stating really clearly that you recognize how vulnerable and generous the other person is being, thanking them for telling you, asking what they need right now.
if you can delay the breakdown long enough, you can have it with a friend or a journal or a therapist.
i think people get into this cycle where all of their tough conversations turn out badly and then it's much easier to panic when the next tough conversation starts.
but when you break that cycle, you'll find out that (while they're still tough) these conversations can actually make your relationships feel stronger at the end. they can make you feel more confident that you know what to do. they can build trust.
it takes a lot of learning and practice to get that way, but dealing with this stuff is probably the best first step towards getting there.