Generally speaking, only race horses are backed in the UK at 2yo. Most TB breeding lines have not yet muscled up enough to take the strain of a rider. That's partly why he is uncomfortable. He's still learning to carry and balance the weight of a rider.
You didn't mention your weight - are you a big or small girl?
Most ex race horses in the UK need re schooling after being discarded by the racers. In any case, they were only ever schooled by the trainers to run in a straight line. Of course, they were also ridden in a different shape of saddle by a light man merely perched up on top.
The saddle will be an issue too, the shape of the back will change rapidly over the next year and so should the shape of the saddle to match - make sure it fits properly.
Presumably you lunge the horse - that will help with the muscling.
Don't forget to work each side evenly.
Then if you are going to ride it out eventually start introducing obstacles
- things like bags, bins, signs you name it, anything which spooks.
But at this age, I'd be doing a lot of work in hand. I'd lead the horse down at his level - so he could see me and not just feel me up on his back.
Then when I did go out, I'd always go with a friend - who preferably had a nice calm older horse who knew the ropes.
British TBs can be skittish, and very sensitive. Don't forget there is a lot of inbreeding in horses bred to run fast.
You need a book - a 2yo horse, is barely out of being called a foal.
Take it easy and slowly