Popped Pimple Possible to Turn into Cyst-like Bump?

I would agree with Dr. Oppenhein and have had one of these myself. They are commonly caused by minor trauma such as biting or even from braces. Occasionally they rupture and clear fluid emmanates from the cavity. They often require excision as definitive treatment.

The bump you are seeing is most likely either post inflammatory due to a resolved or traumatized pimple,  a cyst, or a scar. In all of the above scenarios, it is worth showing to a dermatologist to confirm as each possibility carries a different treatment approach.

Without viewing your photograph, this sounds like a mucous cyst of the lip. This is caused by an irritation or plugging of the minor salivary glands of the lip. It usually occurs on the lower lip slightly inside and often laterally. I might speculate that your chewing on the inside of the caused the irritation leading to this problem.
Mucous cysts,as the name implies are filled with mucous, but are not true cysts, so some pathologists prefer the term mucocele.
Whatever it is called, your problem can be remedied quite easily. I would see a dermatologist, plastic surgeon or oral surgeon and have the structure excised. Mucous cysts tend to wax and wane, but unless they are removed they don't go away on their own volition.