What would you do?

Hi! So I’m 35 weeks pregnant tomorrow. I had my last doctors appointment on Monday. However this was my first appointment with a new doctor cause we just moved. Before that appointment it had been 5 weeks without an appointment(there was a miscommunication between doctors offices that’s a whole other thing). I missed my growth scan and I have no idea how the baby is doing. So I go to this new doctor and they are basically just trying to get to know me. There wasn’t much to do with the baby. The doctor pulls out a hand held ultrasound machine, and I can barely see my baby at all. His heart looks good and that’s about all we can see. After that the doctor tells me at 36 weeks we will start doing weekly appointments. So for this next appointment I’ll schedule it two weeks out and then the next one it’ll only be one week intervals. Well I go to reception and schedule it and my doctor doesn’t have availability for three more weeks... at that point I will be 37 weeks. Am I overreacting or is that kind of ridiculous? I also have hypothyroidism and need my blood work done every so often to make sure my levels are good with the medication. I’m tempted to call on Monday and ask if I can get an ultrasound by anyone who will do it and my blood work done. Does that seem necessary? What would you do in this situation?