Hi Chance,
I can relate. My mother has been very ill for the past two months, and I've been doing the same dance with my husband of 12 years. I'll tell you what (little) I've learned, and you can decide whether it's helpful or not.
I'm not always sure what I want "support" to look like. Sometimes I want my husband by my side, sometimes I want him to stay home and clean the bathroom, and sometimes I just want him to leave me alone with my sadness and confusion. In our relationship, it's better for me to do a little self-diagnosis and then ask for what I think I want, rather than waiting for him to offer what he thinks I want. The other day, when I was very upset, my husband said, "It will be all right." I replied (relatively calmly), "But you don't know that." He was extremely hurt because he felt I was rejecting his offer of comfort. This was not a big deal--it passed very quickly--but you can see how different his take on "support" can be from mine. He wanted to reassure, I wanted to vent.
Right now, I'm not sure how seriously I take your comment about feeling ashamed that you got married. During my mother's illness, all sorts of thoughts have run through my head about my husband, the course my life has taken, etc. I would bet that's pretty natural. When you're under this kind of stress, everything seems wrong. Even if your husband is a pretty wonderful guy, he's not uniformly wonderful, and flaws get magnified under these conditions. It's also even harder on your relationship that you haven't been married very long.
One more thing. Part of your husband's discomfort--which may come across as boredom or disinterest--may simply be that he's uncomfortable being a "spectator" to both the facts of the situation and the emotions those facts engender. Given that he's young, his reaction might be to simply avoid a situation that makes him uncomfortable--and it's possible that it may make him so uncomfortable that he wants to get out more than he wants to support you.
In my own situation, most of the time I have not asked my husband to come with me to visit my mother. My mother was in intensive care for over 30 days. That type of hospital visiting consists largely of sitting around. Only one or two people can visit the patient at any given time. I didn't really see the point in dragging my husband 250 miles to sit in a waiting room. During my mother's transfer to another facility, I did ask him to be with me. That was a 12-hour day involving quite a bit of driving, and I wasn't sure that I would be OK by myself. He came with me and did not have an attitude.
So I would say, ask for what you want, and try to understand that this might be very uncomfortable for him. And try to keep the "big" thoughts--why did I marry him, do I really want to be with him, etc.--for a calmer time. For now, take care of your responsibilities and yourself, and let him help as much as he is able.
I wish you strength. I know how tough this is, and my thoughts and prayers are with you.
best,
daylily