Yeah my thyroid is messed up in all this too, although that's a long story. But I'm now on both T4 and T3.
I don't understand, Starfish, when you say 'I'm not having a cycle because I was put on the progesterone pill'. Remind me what you are taking? Are you taking utrogestan as well as a synthetic progestin? Or just the synthetic progestin?
If you're taking a synthetic progestin, then it will most likely be suppressing your own ovaries and it's less likely that the estrogen is from you - although the effects vary depending on the pill, with some more suppressive than others. (Desogestrel prevents ovulation and is more suppressive than levonorgestrel for eg.)
But it's really not surprising your progesterone is low if you're on a synthetic progestin. Most of them prevent ovulation, that's how they work. If you don't ovulate, you won't produce any progesterone of your own. Progesterone is made from the corpus luteum at ovulation. There is no corpus luteum without ovulation. There is no ovulation on the majority of synthetic progestins... That's how they are birth control.
Really if you want to balance your hormones and get some body identical progesterone, you need to take utrogestan. You can take that as well as the synthetic progestin if you want although ideally you wouldn't. Why are you on the progestin?
As for the testing, the best option I think is the Tasso Female Hormones test with Randox Health. It costs about £45, you do it at home and because it takes blood from your shoulder/arm, it avoids the issue of finger tip contamination. So as long as you don't put gel on your upper arms, you will avoid a contaminated result.