FMLA/ Reasonable accommodation

I am with FAA. We recently got new managers. For the past two years I have burnt through my sick leave to where I have 4 hours left. This is due to appointments and issues surrounding recurring blood clots (DVT).
Long story short I am being transitioned to warfarin but it requires regular-ish blood testing first few weeks until they dial in the correct dose.
I have requested FMLA from my hematologist who said “your condition does not require leave from work”….despite me needing to drive 35 min to get blood drawn, wait, and drive 35 min back every few days.
That being said I also have been sending emails to my new manager (I am not in a new job but they rotated out managers due to reorg) about getting a reasonable accommodation to telework the days I need to go to lab. I am only allowed to work between 6 and 6, I have three kids who go to school and take the bus at 7:15 and most days I need to pick up my 7 year old from daycare unless he rides home with his older brother on the bus.
My sick leave would be tapped out to zero week one with no telework accommodation. With telework I can get in an hour extra in the morning and 30 min in the evening on lab days which would be a lifesaver and make me not need to take LWOP (I don’t even know how that works since my hematologist refuses to help with FMLA)
My boss has been ignoring all emails having to do with this request. (He is answering others)
What do I even do?
And no their dad can’t take the kids to school- he died in 2022 and family is out of state.
I don’t feel this is an insane request but maybe I’m stupid. My job is 100% on a laptop by the way.