I'm sorry you're having to deal with this situation. Most of our insect questions deal with insects on plants, not in leaky bathroom pipes.  However, one of the first steps is to identify what's biting you. Have you collected a sample and called a pest specialist for identification? You said you think they are midges. There was a similar question asked at the extension office in Maryland and this is part of their response: 'Biting midges tend to breed in salt or fresh water sites that are high in organic matter, so unless you have a lot of house plants, they are likely not breeding in your home. They might be breeding in your gutters if they have not been cleaned out recently. Biting midges numbers peak during the summer and the adults die out with the first hard frost.' 

Purdue University has an article on midges that might help you learn more about midges. Here is a link to the article: https://extension.entm.purdue.edu/publichealth/insects/bitingmidge.html

Penn State University has an article called 'Is Something Biting Me' which offers information on possible pests. Here is a link to the article:
https://extension.psu.edu/is-something-biting-me

Again, the first step would be to positively identify the insect that's biting you. Unfortunately, we cannot recommend any pest care specialists.

Are you also working with a dermatologist? They might be able to steer you in the direction of someone who could help you identify the insect. 

I hope this information helps steer you in the right direction.