After the second time (with a condom), we noticed bleeding, too. I thought that maybe I had been cut by a fingernail
I have noticed that rubbing/mild self-stimulation not on the sore area, but slightly above near clitoris, quickly eases the pain for a bit (enough not to leave the bathroom with a terribly pained look on my face).
That's the thing, though. This is a severe amount of pain, while the itching feels similar to mild yeast infections I've had from antibiotics.