Please stop using the Neosporin ASAP. It will ruin the scales which leaves a possible opening for infection. If you want to wash her I would suggest one of two methods.

First you can put a drop of baby shampoo in a bath of water no deeper than half you snake's height. Make sure the water is right at 80 degrees. A couple degrees warmer is better than a couple of degrees cooler. Water temp isn't something to mess around with and should be measured with a temp gun or other digital device. Don't just let her swim in the water. Use it to wash her down, and then get her out and dried off as quickly as practical. Most snakes do not enjoy this...yours might, most don't.

The second way to bathe your snake is to purchase some unscented baby wipes. Warm the wipes up to at least 80 degrees the best way you can (I use a heating pad), and wipe your snake down from just behind the head to the tail. This is my preferred method for bathing a snake that has crawled through it's own feces or urine. It should work in your situation.

You need to do what you can to get your humidity up into the 50%-60% range.