I (female) have some pain with urination the day after sex. Is this just friction at where I pee?

Pain after sex. May be. In that case, the pain is not in the urethra, where the urine comes out, but when urine drips on the lips. Buy a paper chemical strip that checks for urine infection at the drug store. If in doubt, the best thing to do is to have a urine culture done to see if you have a underlying bladder infection, that can be exacerbated by sex.
Might be. A common cause of dysuria or burning with urination or peeing is pfhd or pelvic floor hypertonic disorder. The pelvic muscles which surround the vagina and also affect the bladder opening, can be high tone, or spastic. This condition is typically worsened for a day or so after intercourse. If no uti, consider this condition.