Zoe I'm a lot older than you, but here's my experience.
I've had four teeth out and it didn't hurt getting them out, although my mouth ached a bit for a few hours after the numb feeling went away. I took pain meds for a couple of days and was fine. It's important to follow your dentist's instructions and hopefully you'll find this is okay for you.
Getting braces was not sore at all. I was very nervous ... being 47 years of age didn't help, but my ortho was great and explained everything well. It didn't take long and after instructions about cleaning my braces and teeth and a practise with the oral b floss, I went to a cafe and enjoyed lunch. I'm one of those lucky people who've not had any pain during my treatment, but I've had a little discomfort at times, but nothing that wasn't quickly put right with a pain med, or simply forgetting about it.
I'm yet to experience getting my braces off, but I've had a few brackets moved and the only pain, was my tooth feeling sensitive when the old bonding material was removed. This was coz this tooth was loose and had been doing loads of moving. I've been told that your teeth are more stable when it's time to get your braces removed.
Is it annoying having braces? ... an interesting question. Most of the time I don't reckon so, but a lot of that is to do with your attitude. I reckon that they're as annoying as you let them be. My life is too full and too busy for me to spend time thinking about them, so the only times I really focus on having braces is when I'm eating and brushing. I've never had my eating afffected by having braces and was eating the same foods I had pre braces, within the first week. I'm aware that food sticks in the brackets, so I drink water to rinse most of it out when eating. Other than that, they don't warrant much effort at all.
Good luck with having your treatment while you're so young!