Can certain medications cause a person to become anemic

Yes: The mechanisms and known culprits are too numerous to list here. Methyldopa famously produced autoimmune destruction of red cells ("coomb's positive anemia", only the best known of several drugs); Chloramphenicol predictably lowered the red count, sometimes permanently and fatally, and very high doses of penicillin will destroy red cells. Physicians are alert to this. Good luck.

Certainly: Many chemotherapy and related drugs have always been associated with anemia. Aspirin, Ibuprofen and other nonsteroidal agents can lead to anemia by causing bleeding in the stomach. Certain antibiotics (penicillin, bactrim) can damage red blood cells causing hemolytic anemia in predisposed individuals. Some drugs indirectly cause anemia by via kidney or liver failure as an untoward side effect.