I know that lack of intimacy problem pretty well, I've been devoid of any physical intimacy (including snuggles *sniff) for over half a year now. However while I fulfill 1-3 and can't say anything about 4 since you didn't mention where you live, I'm male and thus don't qualify as your girlfriend.

But congrats on new friends, starting therapy and especially good cookies! (Oh, and I advise against self-medication with hormones, but I guess you'd expect that.) Maybe you can find another clinic or laboratory that can check your hormones on shorter notice? You might be required to drive around the country a bit, but I guess in that case it might be worth it? Grab a phone, asking is usually free.