I'm allergic to penicillin. am i also allergic to penicillin derived antibiotics?

Maybe: Penicillin allergy is usually secondary to either the beta-lactam components or the minor determinants. If you are found to be allergic (via skin testing) to the beta-lactam component then you are at risk for sensitization to all beta-lactam medications, including cephalosporins. Fortunately in the majority of people, this is not the case. You should consult with your local allergy specialist.

Yes: Good (and important) question. If you're allergic to penicillin, then you should not take its cousins like Amoxicillin and dicloxacillin. There's a certain amount of cross-allergies to the cephalosporin family too.