If she didn't perform oral sex on you, or you didn't have sex with her, and her vagina didn't touch your penis, you can't have an STD. Towels don't transmit STDs (nor do sheets, etc.).
You could, however, be having a reaction or have an infection from the oil getting in your urethra. Depending on the pain level, you might want to see your doctor soon for this. If it's not bad, try increasing your water for a few days and see if you can flush it out, then go to the doc if it doesn't improve.
Remember that guilt doesn't equal risk.