From the photo, it appears that the overbite is not that problematic, but there may be a cross-bite issue. This is when one arch overlaps the other in a way different than normal. Often this is developmental and has a TMJ component to address.
It may be possible to expand arches and use braces to get things to line up, but without back molar teeth, it may be a challenge. Some orthodontists are using temporary implants to get the leverage they need, and that may be necessary for you.
I would suggest a consultation with at least one orthodontist. As you consult, remember that in GENERAL, an orthodontist sees solutions by moving teeth, an oral surgeon sees solutions by removing teeth, etc. Meaning simply that whatever the main focus of a practitioner is, that tends to be their advice. It is possible your dentist simply sees a solution he is more familiar with and that there are still options.
Or not. :)