It may be time to take a break from your relationship with A for awhile. At least until A starts acting more responsibly about the B situation, and preferably until you've had ample to time to contemplate if A is really a good partner to come back to. I wasn't 100% clear on all that was described in your original post, but I did get the idea that A is putting you on hold while putting B on a pedestal. That's all well and good taking NRE into account, but when STIs and unsafe sex enter the picture, it is much, much more serious.
If you do continue going out with A, be aware that you're likely to get 2nd-class treatment (followed by the obligatory fight, apology, and assurances that things will be different next time), and protect your own health, probably by refraining from doing anything that even *might* result in you getting an STI. And any other partners you have, you have to keep them updated on A's behavior, as their health is at risk too.
What I'm tempted to say is that it's time to cut the ties with A for good, but if you're too emotionally invested for that at this point, at least take steps to protect yourself, emotionally and physically. Change your expectations. You know how she's been acting. That's not likely to change any time soon, if ever. You can't change her actions, you can only change your own actions.
Keep trying to communicate as much as possible, but remember that communication doesn't work very well unless all participants are being 100% honest. To me, it sounds like she's not being 100% honest with you. That's a red flag.
I hope you are able to get to a better place, and take good care of you.
Love means never having to say, "Put down that meat cleaver!"