
I'm guessing he has black nails if he's a Westie? Always more difficult to clip because you can't see where the "quick" (the blood) supply ends as you can on white nails. I walk my dogs on the road a lot , so they rarely need their nails clipping (one way of avoiding having to clip!) It's a good idea to get him used to having his nails cut from a young age. Ask your groomer to show you how to do it - or your vet will do it & buy a pair of nail clippers - I find the guillotine ones easiest. If you're not sure, just nip the very end off, you'll probably find that's a lot thinner anyway.
If they are not kept short, apart from being painful to you (as you've discovered), they will just get longer & longer & are not good for his feet as his toes will begin to spread (pet hate of mine :( )
If you don't want to cut, you can file them, but someone else will have to give you info on that.
IN my breed, we also trim the hair between the pads, keeps the feet tidy & also saves some of the mud being brought into the house.
HTH