Flushing on its own

Sounds like your flapper has to be replaced. Take some colored egg dye and put in tank and see if it leaks into the bowl.

I haven’t tried your suggest yet, but that makes logical sense. My only concern is that I just bought a whole new everything including the flapper. Is there a way to see if it can fit tighter or is this something that I need to pay attention for making sure that the flapper actually is going to fit my toilet if I were to buy a new one?

I just had this same problem. I bought a new toilet and the flush valve was not seated properly. If you don’t want to buy a new flapper, try this method to isolate the source of the leak. Shut the water off to the tank and mark the level of the water inside with a pencil. As the water recedes mark again. If it stops above the flapper then you probably need a new flapper. If it continues below the flapper most likely it will be the flush valve. Also, if the tank is not level, that could cause leakage.