Can you still be treated for most infections if you have a penicillin allergy?

Yes: Despite increasing antibiotic resistance, there usually is another antibiotic that can be found. If this is not the case, and there is a serious need for penicillin, many penicillin allergies can be desensitized. This procedure takes place in the hospital and only lasts for the duration of time that you are taking penicillin, but is effective. So in emergencies, there are still options.

Yes.: Almost all infections are treatable with non-penicillin antibiotics but if you develop an infection requiring penicillin, then you can be admitted to a hospital to undergo desensitization, a procedure which over a few hours "teaches" your body how to tolerate penicillin. Desensitization will allow you to tolerate a full course of penicillin but once stopped for 24 hours the allergy returns.