I wouldn't worry. He would have to specifically order a drug screen blood test to check for drug use, and unless you gave him any reason to suspect you're a daily smoker or told him you smoked weed, he wouldn't have any reason to do a drug screen.

Allergists/immunologists order specific allergy blood testing, and I found this link about that. I had the very same blood tests done last year. Basically, they look at your antibodies and particularly at your levels of immunoglobulin E (IgE), which go up in people with allergies. He'll probably do skin tests, too, if he hasn't already. (Mine did, and I was allergic to every type of pollen there is, practically.)
http://www.webmd.com/hw/allergies/hw198350.asp

As far as confidentiality's concerned, if you're 14 or older, in most states he's supposed to keep the results of any tests confidential between you and him, but they don't always do that with patients who are minors, particularly if parents come straight out and ask them direct questions about their kids' test results. Again, it's very unlikely he ordered a drug screen, so try not to worry. Let us know how it turns out!!!