Swelling in the feet? Where? Hooves don't swell, hence the extreme pain with laminitis. With having growth rings, the horse may have some founder issues, so be sure to not overfeed grain or legume hay. Exercise is good. But nailing shoes on and it hurting, with the growth rings, makes me think he's in a bout of laminitis and no wonder it hurt. Imagine if you had smashed your fingertip with a hammer, and in the midst of this throbbing, someone is trying to pound nails through the tips. OUCH! Poor guy.
A hoof that's been neglected doesn't accurately reflect the way his hooves would normally grow, so lopsidedness is no reason to shoe. If he has some toeing in/out in a mature horse can't be fixed if it's in his leg conformation, so shoeing him "straight" could do more harm than good, potentially.
At least you are pro-actively seeking help for him, so I can't fault you for that, nor can I fault you for trusting your farrier,like you should usually, nor him, for wanting to shoe-it's what he has been taught to do, even with laminitis. Just know you have other options, that I hope you will try! I see so many good results with barefoot trimming, that I can't remember now why I thought shoes were so great, and even with EXTREME founder, a lot can be done with a trim and some boots! Pat on the back for you for getting his feet taken care of, regardless. Anything is better than neglect!