Probably unhelpful as not very knowledgeable about dentistry/orthodontic practice but...
How old are you? As long as you're in full time education and 18 or under I'm sure you can get them done. I had a similar issue, had twin block (jaw aligning) braces at 13, when I reached 17 (being more self aware) I realised they still were pretty bad and wonky, was sent to many orthodontists for help, some rejected me, then when I was 18 I went to one and said how they were getting me down, and they gave me train tracks for free on NHS.