What do you mean inconclusive? if it was a "faint" positive it still counts as positive. You can always just go to the doctor to get some blood test, but first wait until your period is due.
A women's ovulation time (in a normal cycle) is about 2 weeks AFTER her period, so you didn't have sex during your ovulation time, but since you DID have unprotected sex it's not impossible, however it's highly unlikely. You wouldn't be feeling symptoms a week after unprotected sex, maybe 3-4 weeks, but not 1. You can wait another week and take a first response early response HPT, or wait until your period is due and take a HPT. Good luck!