I am thinking maybe some lessons, and a trainer to help you.
Do you do any ground work with him? If not you should be, get his feet moving on the ground and get him thinking. When he gets excited he stops using the thinking portion of his brain and is using the reactive side. You need to learn how keep him thinking and listening. But if your falling off then maybe some lessons will help you keep your seat and get your horse more confident in you as a leader.
Yes definitely get some lessons so the problem doesn't get worse. Try and stay very calm and relaxed yourself when in the saddle so not to make him nervous. Your trainer will be able to advise you on methods to calm him. If he has had the training, then it is likely that you just need to learn to ride him, and push the right buttons. Not saying you are bad at riding, but every horse is different and you will get used to him! :)
You say he gets excited... what exactly does he do? If he's just jigging around, you REALLY need to work on your seat to get some balance. If he's bucking or spooking, then try riding him in a smaller, enclosed area and do some ground work before you get on to get him brain going. Then once you are on, go straight to riding some baby leg yield/turn on the forehand. Get control of his brain before you start working his body.
I'm going to second what everyone said about doing groundwork. You should not be riding this horse until you have his full respect, and have a better seat as well. I will also second what everyone said about you needing lessons as well. If you can't sit a out a spook then you seat needs to improve, especially since you have an excitable horse. Is that your boy in your avatar by the way?
EDIT: Sorry just read that you have taken lessons. I suggest you ask your instructor for exercises to improve your seat. I'm sure you can find something to do on and off horseback to help you :).
Get the trainer to work WITH you and the horse, not just the horse.
He is 3, I think maybe very nervous , diet maybe rich, no horses around, and you sound like maybe you are young? Those are all elements that add up to explosive forces.
I think he needs more ground work, too, but you would be best to have an experienced person help you with that for a bit. Sounds like too many challenges all together for a good outcome all alone.
Yes that is him in the picture! I do have a good seat! I think it's just excitement maybe... But thank you everyone for replying!
I rode him without a saddle or bridle not so long ago (before with the tack!) He was fine when we walked, trotted and cantered (that was never done with him bareback & bridleless) and I stayed on!!! :)