I believe your betta's fin was damaged by Cardinal Tetra. These nippy little fish do not have to chase the betta all the time to do the damage you have seen on your betta. They just need to do it from time to time.
I highly recommend you to get a separated tank just for the betta. A 5 gallon will do fine although 10 gallon is recommended.
For your question, since you just got the ammonia and nitrite under control. It is a good idea to wait a little longer before adding more fish, and it is the best to add no more than 1 or 2 fish at a time since your aquarium is not that big to begin with.
