What Causes Itchy Rashes On The Arms And Legs?

OUCH - I have been dealing with bed bugs for a time. I have had been getting bit in the same general area for weeks. I must have an allergy because I get bad rash like areas around the bites and they itch SO BAD. I have been dealing with this. HOWEVER!!! I took a warm bath, nothing added to water, and when I was getting out the areas with the biggest concentration of bites along my wrist to elbow and my legs ((not so many bites)) began to burn like a chemical burn...it is burning SO BAD - I cannot get it to stop. I patted myself completely dry with paper towels to avoid rubbing the area, and applied a whole tube of neopsorin with pain relieving cream...it is still on fire! I am on city water, and it does have a chlorine smell from time to time. My young daughter who has no bites took a bath before me and has no reaction. I do not know if it is from the thinning of my skin and scarring in the areas or what - it is hurting REALLY REALLY BAD. I do not have insurance and the clinic said they don t know what could cause it and would have to run tests each test is al a carte. The minimum payment will be 250.00 plus any scripts they prescribe. What can I do - I cannot run it under cold water because the FREAKING water started the burning!!!! HELP! I am not taking ANY medication, or supplements and do not drink alcohol, smoke or do any type of drugs. IT IS BURNING!!!