Just a few words about the amount of risk involved, since I completely agree with AuntieJesse on that it is unlikely you got a STI.
It is very hard to give exact numbers for the risk of transmission: there are too many variables involved. When we say "low risk" what we mean it is much lower if compared with unprotected vaginal intercourse. We are not juggling numbers like 0,1% or 10%, since such estimations are always inaccurate.
You can get syphilis if your partner is infected, if he or she is in primary or secondary stage of disease and if you come into a direct contact with a syphilis sore, and if the contact is strong. And if all those ifs are true, the risk is 30 to 60%. And, given how uncommon syphilis is, if we apply the statistics to a random oral encounter with a CSW in the US, the numbers go down to well under 1% (but we still can't say if it's 0,1% or 0,001% for both numbers are very low).
To get gonorrhea you need for the germs to infiltrate your urethra and the risk during unprotected intercourse is quite high. Gonorrhea of the throat is by far less common, so we can only assume the risk to get it from giving oral sex is low.
You got the idea. Hopefully it puts your mind at ease.
Your risks are quite low for giving oral to a vagina. The risks there would be mostly syphilis, and that's uncommon in most developed countries. I wouldn't even worry about it. She'd have to have a sore in order for you do get it, and you'd get a sore on your penis, but again, it's uncommon and low risk with oral on a vagina.
From receiving oral, your risks are gonorrhea, chlamydia, NGU, syphilis and herpes type 1 if you don't already have that. The red spot south of your navel is most likely unrelated. The redness on your glans could be a fungus, irritation, or a wide variety of other things, long before an STD. The risk for an STD from oral is lower than with penetrative sex.
You can't get tested for STDs anonymously in most places. You can go and self=pay, and leave it off your insurance, though. Any STD clinic or Planned Parenthood will allow you to do that.
I doubt this is an STD, though. Get checked if you have a partner you are concerned about, but if it's negative, and the symptoms remain even after hydrating, get checked out by your regular doctor.