I am renting with male roommates. Previous tenants were all women, they moved out last May. Our toilet pump had a tampon stuck around it. Could this have been flushed months ago and just now causing problems?

Its possible but I say the odds are low... have any of your male roomates brought a female into the home who might have done it?

Ejector pumps are not designed for sanitary product removal. It could have been there for a while and now just got caught as it decomposed.