Can I drink alcohol while taking penicillin?

Not recommended. I do not know of a specific interraction, however, when you are sick enough to take an antibiotic, alcohol may worsen your illness with dehydration, nausea, upset stomach, headache, lethargy etc. Drink water or an electrolyte replacement.
Yes. No problem taking penicillin class antibiotics with alcohol but keep it in moderation. If you have a significant infection it would be best to abstain until the infection has resolved.