I think to be on the safe side, I would get him to be examined by your vet. If the stick did catch his eye, it could cause trauma and potentially an eye infection. Given that he is an older dog, any infection may take hold, causing more damage, possibly permenantly. This was an accident, so don't beat yourself up over it, but do try to get him to your vet who may wash out the eye and prescribe some anti-inflamitory meds. Tony
If he will let you, look to see if there is anything in his eye. It sounds to me like one of two things happened. #1 he may have a scratched cornea, which you can't treat. It will heal itself in a week or so. #2 he may have some bark/wood stuck in his eye. If this is the case he needs to see a vet. If you have a vet ophthalmologist close to you, and it isn't better in the next week or so, call them.