Burning alone with out discharge might be irritation from lubricant, especially if you used condoms with the spermicide nonoxynol-9. You clearly could not have acquired an STD that would cause urethritis with the exposures you describe, i.e. if the condoms were properly used. If you can't see any discharge, even early in the morning before you urinate the first time, then I suggest just sitting tight and not worrying about it if the symptom goes away. But if it continues, or of course if you see abnormal discharge, you and your partner should both get examined.
Or if you just want reassurance, you both could go to your local health dept or Planned Parenthood for STD screening. Your partner might appreciate the gesture: she has been tested recently, so why not you? Do it together as a partnership thing.
"Paranoid" isn't the right word, but anxiety is a good explanation for much of what you describe. Relax. You have done everything right: you got to know your partner (at least a little bit) before hopping in the sack, spoke with each other about STD risks, and are using condoms. Your risk is very low. If everyone followed your path, most STDs would simply fade away. If you're going to worry about this sort of exposure, you'd better plan on being celibate--which I don't recommend for anybody.
Good luck-- HHH, MD