I looked into all this a while ago, and I will say what I remember, but I am no doctor.
First, how much a condom protects is controversial, and a lot of the discussion is what you mentioned, the skin at the base, below the edge of the condom!
Different STDs are transmitted differently. Diseases like HIV, chlamydia, Gonorrhea, for example, are spread by bodily fluids and they infect the male by entering through the urethra or an open sore. For these diseases, a condom is thought to be pretty damn effective.
Other diseases can be spread by skin to skin contact, for example herpes or HPV. So, for example, if a herpes sore comes in contact with your skin at the base of your penis, or scrotum, transmission is possible.
In your case, a condom is meant to prevent disease transmission through bodily fluids, and I don’t think it matters if that fluid is blood or vaginal secretions. In that sense, you should be no more worried than if she was not on her period.
The problem is, even when you use a condom, afterwards you can still have doubts in your head and worry that you might have been infected. And you are right. The condom greatly reduces the risk but does not eliminate it. And you can read 1000 pages on this topic but you will never find the answer “did I catch something from her” without getting tested.
I am married, and I have frequently traveled to Mexico, where the strippers are very young, beautiful and inexpensive. I have often been tempted to go down there and have a fuckfest, but I never have. For a married guy, the risk of catching something is more than just a disease problem. It would be my life, family, home, etc. A condom does not provide enough of a guarantee for me to risk all that, just to fuck some strange pussy.
If you are looking for a more definitive answer, you will not find it without getting a test. Although it seems silly to practice safe sex and still go for a test every time you have sex, that is the only sure way. For most people, if they used a condom properly, then that is assurance enough.
Horny Bastard