I had both. The blood test told me I wasn't allergic to dogs which was a great relief.
The T.R.U.E. patch test (No scratching or pin prick) tested 29 different chemical or metal allergies. I did not have a test for food allergies. I know I am allergic to fresh tomatoes.
My tests showed 4 different allergies. Nickel, Caine Mix (Benzocaine, Lanocaine, Cocaine etc.) Colophony (Wood resins) I have severe contact dermatitus to pine etc. requiring Prednizol, injection and pills)
Personally, I doubt you got sick from the tests. Maybe from another sick person in the waiting room. Take a couple grams of Vitimin C before you go next time. I picked up a cold sore at the doctors office. VC and ethel alcohol swabbed on for an hour took care of that. The doctors office was the only place I could have gotten the cold sore virus, I don't go out much.
Ask about the TRUE patch test. It sticks on like a piece of tape. No showers for 4 days and it might itch but that's the worst of it.