Dear Destinygirl: If there is a single isolated area which appears to be bruised it MIGHT be a varicose vein of the labia. Alternatively one can get a bruise in the labia from a small broken blood vessel. A spin bike seat or fall onto bike bar can create bruising. If you have easy bleeding (eg from shaving cuts, bleeding gums, etc) even minor trauma can leave bruising.
It would be very uncommon for a soap irritation to impact just one side of the labia. You can certainly try discontinuing the soap. For the most "for sure" answer you should get a visual exam of the area from a GYN or local family planning clinic. Certainly if the involved area appears to be enlarging you should gte seen.
Yours,
Jane