Yes, without a doubt. Ammonia in a tank means that the cycle isn't keeping up with the waste but is not an indicator whatsoever in tank stocking. Fish need room to grow and swim. This size tank you have with the type of fish and the number of fish, doesn't allow either. There are some testing like nitrates that are an indicator but there are other things in the water that are not tested and have an adverse affect on your fish.

I am sorry to tell you this but there simply is no solution to your tank situation except to get a larger tank or to return your fish and get other fish that are suitable for your tank size.