In short, to answer OP's original question: Yes, it is theoretically possible for your wallet to generate an already used address, but our sun will have engulfed the Earth long before that ever happens.
I was once curious about Op's question. Though OP wasn't clear to me until I read your reply.
Before I visited the technical aspect of OP question, I was ordinary consoled by the fact that the address is alphanumeric, which will make it impossible to coicide.
But later I learnt that the strength of secp256k1 is about 2^128, and it's proven that anything higher than 2^90 is very much secured.
But I also ask if the blockchain doesn't have an algorithm to immediately detect an attempt of duplicate upon generating a coincidental address. Maybe this will be needful when the Sun must have engulfed the Earth according to o_e_l_e_o.