There are various options:
1. Credit card installment plans - certain clinics have pre-arranged plans with the banks such that credit cards from those banks are allowed to enjoy interest free installment payments (the whole amount is charged on the card, and then the patient pays monthly to the bank).
2. In-clinic installments - I have heard that some clinics do allow direct installment payment arrangements, and as such, you would probably need to message a few more dental clinic to find out the possibilities about this.
It is after all not a life-changing or life-threatening condition, so a more sensible approach may be to just leave it alone for now (if it’s not causing major medical issues), and to go for the necessary surgery or braces only when you are working and able to finance them .