To have your progesterone drop to 3.8 after the loss can be normal as your hormones drop when the miscarriage starts. And it can be totally normal thing to have happen. Many doctors don't feel progesterone is an issue because to them, low progesterone levels in pregnancy mean there's something wrong and the body is doing what nature intends to correct the problem. It's very possible this particular pregnancy had genetic issues or poor implantation or just wonky cell division and your body did what it had to do. And unfortunately, most doctors will approach one miscarriage as 'just bad luck' and won't send you for further testing (unless there's reason for it-eg. family history of recurrent loss or health issues that can contribute to miscarriage) unless/until you've had 3 or more losses. I had to go through 3 before I got any sort of RMC testing done aside from checking my TSH number and doing a CBC. As heartbreaking as it is to go through a loss, there are very valid reasons for waiting to do testing-the biggest being that most women will actually lose a pregnancy at least once in their child bearing years but they are completely healthy in every way and go on to have normal pregnancies after. My sister is one of those women, my mother-in-law had a loss, my sister in law had 2, one of my dearest friends has had 2 as well. Yet all of them have gone on to have normal pregnancies after without complications. So to have testing done now may only be a waste of money because you very possibly could have no physical reason for the loss-it just happened. It sucks, I know, especially when you want something SO bad and then you lose it in such a heartrending way.
I guess what I'm saying here is I understand both sides of the story here and I get what you are saying. I totally agree that what the doctor said was completely uncalled for and utterly disrespectful but I also see why she's saying it doesn't pay to do testing right now. Does that make sense? It doesn't minimize your loss or make you want to get tested for everything to find an answer and a miracle pill so it doesn't happen again any less. But it is sound advice even if it was delivered in a very mean way.
As for the insurance part, don't listen to her. She doesn't know much about health care if she's saying stuff like that.
As for your progesterone level, I'd ask your doctor to test you 7 days past ovulation to see what your numbers are. That will show if you have a naturally low level post-ov when it should be elevated, indicating that you've ovulated. This means tracking your cycle with opks and other ovulation indicators so you can hvae the test done at the right time and waiting for your first normal AF after the loss so the miscarriage isn't causing hormone fluctuations any longer. It's also a good idea to get it tested in early pregnancy so the doctor can see if it's rising normally during the pregnancy. For me, my progesterone is normal at the start of pregnancy but it doesn't rise like it should as the weeks go by and I need to supplement or I'll miscarry. That is why I take progesterone pills.
Sorry if this is such a long reply but I want to make sure you have plenty of information so you can decide where you want to go from here. I would recommend you find another OB though since that one seems like a piece of work.