If I create another Bitcoin address in my wallet, how can I be sure that this address has not been created by someone else?
Probability. The odds of two people who generate random addresses actually generating the same address are not just "astronomically unlikely", it is beyond "astronomical". For all intents and purposes, you can just assume that it's impossible.
I mean, creating a new address seems instant, what if someone else also has created the same address at around the same time.
What is going to happen then?
It is nearly instant. Your wallet just chooses a random number for the Private Key, and then quickly does some Elliptic Curve multiplication to generate the Public Key. A few quick SHA-256 and RIPEMD-160 hashes later and you've got a Bitcoin Address.
Nobody is going to randomly choose the same address. It just isn't going to happen.
But for the sake of argument...
If it did happen, then you both would receive any bitcoins sent to that address, and you both could spend those bitcoins. If the other person spent them, they would disappear out of your wallet.