18 and in need of braces

I'm currently a sixth form student awaiting my exam results before I head to University. As it stands, I've been on the waiting list for braces since 2021. I've had 2 past referrals but one amounted to nothing and the other resulted in the 3 and a half year wait for an orthodontist appointment, which will occur Mid-May 2024. I have heard that if you're on the waiting list for braces pre-18, they will not charge if you're eligible for them. However, I'm writing to ask about my options regarding braces as I'm unsure if I fit into the "needs braces for medical reasons" bracket. If I don't get the go-ahead from my orthodontist next May, then what was my wait for? I want to explore my options and have come to a standstill whereby I either wait til next May (to likely be rejected) or invest in private healthcare, which brings about a whole new bunch of questions. I'm willing to send pictures of my teeth in private if anybody has personal experience in the orthodontist field and can provide a second opinion on whether I should wait for my appointment, or invest in private healthcare for braces.