Hello there, sorry to hear about your horse's spooking problem, I am sure that is very frustrating!
First of all I would recommend a thorough physical exam by your veterinarian. Paying especially close attention to his eyes. A change in his vision will certainly be a cause for spooking, but it is also worthwhile to make sure there is no pain, especially in the mouth or back, that could be adding stress or triggering your horse.
If he checks out physically, I would think this change in behavior is likely the result of having been put on the extended rest period. Behavior problems are often a result of stress and boredom. I would focus on reducing stress and boredom in his lifestyle.
He should be turned out as much as possible and with a companion that he get's along with. Horses are very social animals. and social enrichment is important. You may want to think about toys or other things he can play with while in his stall or turned out.
The other thing to think about is his diet. You are right, excess sugar and carbohydrate in the diet can cause behavior problems, so you are on the right track in eliminating the carrots from his diet. I would try and put him on free choice hay and/or pasture. If he is on free choice forage, he may not even need extra grain or feed. I would eliminate all sugary treats (sugar cubes, apples, mints etc), and put him on a low carbohydrate (low starch) complete feed that is high in fat, if you think he needs extra nutrients/calories that forage alone isn't providing. Avoid feeds that contain corn and molasses.
I hope that helps, please let me know if you have any further questions or concerns,