What to expect after horse's have there yearly shots?

It probably wouldn't hurt for you to give the vet a call just to be sure, but I think the horse is okay. It is possible that the neck is sore from the shots. If so, it may be a week or two for the soreness to work out. They will stagger and stumble a bit if it is the neck. Very scary, but normal. The horse uses the neck for balance. If it is sore they don't want to use it and therefore act as if something is very seriously wrong. Bute or aspirin could help but ask your vet first. (This happened to one of our horses once. It was a sore neck from the shots.)