Yep, as I suspected yours looks basically exactly like mine. The profile picture of you with your mouth closes is almost identical to me!
Actually, I'm surprised they said that no surgery would work for you. Like I said, it looks identical to mine, and I went to 8 orthodontists all who told me they couldn't do anything without surgery. I was worried about my lower lip and I asked if after I'd had just braces on their own whether my lips would then meet and they told me that the movement wouldn't be enough and so my lips wouldn't actually really change position at all. I'm not sure if it will be the same for you, but just something to consider if you dislike that fact about yourself as much as I do!
Also I didn't realise you were England as well. If you do decide you're interested in the surgery, the waiting list actually isn't anywhere near as long as I was told. It did take a little while for me because they lost some of the medical staff and therefore everybody's appointments got pushed back as there weren't as many people to spread it between, then held it up by myself by no longer being sure of whether I wanted the surgery or not so they added another appointment after two months or so so I could come in and discuss it again. The longest delay was for my joint consultant with the surgeon, the orthodontist, and whatever the name of the people who do things with chins is called

But that's understandable. I don't know how it works with you, I assume it is the same all ove the country with the NHS to be honest, but my orthodontist works at the same hospital as where the surgery will take place. From the date I signed my consent form I got given a date of exactly three months before having my braces put in.
I think I've said this already but I was told the same as you about my chin point. They explained it to me quite graphically! In my consultant with all three of them, they told me that at the same time of the jaw surgery he would cut off the end of my chin bone so that it didn't stick out so much. I assume it's probably the same as you, just because our cases seem to be so ridiculously similar haha!
EDIT: Also, for what its worth, the NHS said that they were only willing to go ahead with both braces and surgery, not braces on their own. They said that over a certain distance, any changes that braces could make on an adult would be purely cosmetic and not actually correct the problem, so they were unwilling to do them without the surgery as well. If you haven't already seen an NHS surgical consultant I'd say it's well worth doing. As they are the one who will be doing the surgery on you, they're probably the best people to talk to! Also in my case they gave me a list of what I could do if I didn't go with the surgery and ranked them by what they felt their effectiveness would be. They made it clear they weren't going to fund any of it and stated what all the problems would be with each, but it did help and make my options much clearer - especially coming from the NHS who weren't going ot make any money out of it whatever I did!