Your child's reaction to a sibling getting sick enough to go to the hospital is not really atypical. Even neurotypical kids will sometimes respond that way to the stress of a family member having an urgent illness. Actually, so will some adults.
That your child is diagnosed with anxiety, ADHD, and OCD makes this even less surprising.
Keep in mind you are also experience stress and anxiety due to your other child's illness, compounded by these challenges with your 15 yo. So your reactions may also not be ideal.
I would view your 15 yo's behavior not as "selfish" or even lacking in self awareness, but as evidence of poor coping skills. Assume he's experiencing a spike in anxiety due to the sibling's illness, driven both by fear for his sibling and also a [very normal!] fear of abandonment as he's watched your focus shift to his sibling. Then think about what healthy coping skills for this would look like, and see if you can coach or model these.
For my SN kid, one of the best ways we've found to help her deal with high stress family situations is to take some time to talk it through with no judgment. Even just 5 minutes to acknowledge that a situation is scary, stressful, or is resulting in her having unmet needs (attention, sleep, a reliable schedule, etc.). I listen to her complaints and validate her feelings. Often I will share that I feel similarly, that the family stress is also making me feel anxious or frustrated. Then we talk about ways we can get at least some of those needs met while we get through the family crisis. This process helps teach valuable coping skills and with practice, my DD is now able to initiate these conversations herself without having the tantrum first. It has helped her become more aware of how she responds to stress and that her grouchiness and irritability is often caused by suppressed feelings like fear.
Agree with PP that he's not a bad kid. Your family is dealing with something challenging and he lacks coping skills and has some built-in obstacles to helping him deal with stress.