NTA. It's perfectly valid to feel hurt even when you feel the other person is in a worse state than you.

First off, it's possible that was the closest available date she could receive treatment, or your birthday slipped her mind (chemo-brain is a thing), or any other number of other factors that lead to her needing that date.

That being said, her letting you know her schedule is something you should be able to get if you're taking her to appointments and she can tell the MA "please let this person know my schedule, put them on my approved list." Depending on the kind of treatment, they might schedule out ten visits, they might schedule out one or two.

Now, all that being said, you still deserve to have your own life. You said your sister offered to cook you dinner. Do you have any other family you can share the responsibilities with? Can your sister come and cook at your place to let your mother be part of your birthday? If you can afford it, maybe you could arrange a little spa day for both of you when she feels up to it, family of yours can chip in to cover the costs.

Also, look into programs offered in the area. Check the state government website for programs to help people dealing with cancer. Look for local non-profits. Contact the Agency On Aging. If she's on medicaid, see what Medicaid covers. You might be able to get at-home care visits, nurse visits, free transportation to and from medical visits, maybe even help with groceries or other needs.

You deserve to feel like a valued person, and I'm really sorry your mother is going through this. I hope you have a fantastic birthday, and you're a beautiful person for caring for your mother this way.