I don't think you're being a baby at all, but I think once you're recovered from this mess, a bit of neosporin is plenty to protect you in the future. Just a dab wherever your skin is broken, wouldn't take long to apply.

I had a paper cut the week before the race, and it did worry me a bit. Before the race I slathered it with neosporin and put a band-aid on it. The band-aid came off in the water (my own little contribution to the muck in the lake ), but the cut was as healthy and pristine the day after the race as it was the night before. (I also wore silicone earplugs since I'd just gotten over a case of swimmer's ear from the pool.)

I don't know if you were ever into those sensory-deprivation flotation chambers that were popular in the '80s, but they'd just tell you to put a dab of vaseline on any broken skin, so that the salt water wouldn't burn. It sealed the water out fine.