I'm somewhat confused by your question. If you were the receptive partner in anal sex (bottom), there is no way you could have acquired a urethral infection, unless there also was penile exposure either anally (top) or orally. Or perhaps there were other penile exposures aside from the event you describe?
In any case, your symptoms are compatible with sexually acquired urethritis: gonorrhea, chlamydia, or nonchlamydial NGU. They might be caused by a non-STD urinary tract infection, but UTIs are rare in younger men without underlying abnormalities of the urinary tract, recent genitourinary surgery, etc.
By the way, unless you have HIV infection yourself, I hope you asked your partner's HIV status and assured he is HIV negative. Unprotected receptive anal sex with HIV positive partners (or partners whose HIV status is unknown) is by far the most efficient way to acquire HIV sexually.
Bottom line: See a health care provider about the burning sensation right away. Your local health department STD clinic would be a good choice.
Good luck-- HHH, MD
If the other person was inserting into you, why would you have burning sensations when urinating? I don't think any STDs can get into your system through the anus and then cause symptoms in your urethra.
J