If your eye is still uncomfortable take a warm shower to be sure you don't have hand wash on eyelids. Use artificial tears as often as you want to soothe the eye. Not at all likely to be permanetly damaged. In COVID times common problem.
Would drops for dry eyes suffice in place of artificial tears? I had to wash my hands a number of times to get hair pomade off them before washing out the eye when the hand wash got in. I’m just wondering if any residue from the hand wash got in. I have inserted the dry eye drops into my eyes a couple of times since.