from what you have mentioned above it seems that your front teeth are getting proclined or moving forward which as well might be the reason that you are not able to close your mouth properly. In that case braces would be the best option to correct the same. You need to consult a dentist and get the required treatment planned out.
Suggestions offered by doctors on Lybrate are of advisory nature i.e., for educational and informational purposes only. Content posted on, created for, or compiled by Lybrate is not intended or designed to replace your doctor's independent judgment about any symptom, condition, or the appropriateness or risks of a procedure or treatment for a given person.