Probiotics do offer many benefits from manufacturing B vitamins to immune support. You would not be allergic to the bacteria themselves, but you could have a reaction to things they are combined with such as dairy or fillers and flow agents in capsules. If you can tolerate dairy I recommend going with plain kefir that is allowed to ferment a little longer to use up any excess lactose.
Prebiotics are better than probiotics for the long run though. Probiotics only supply a limited number of the thousands of beneficial strains of bacteria in the body. Prebiotics are the food that feed all of the flora, which in turn stimulates the growth of all the flora rather than just replacing a very limited number of strains. Prebiotics are fibers. My favorites are rice bran, oat bran, and FOS.