You can do it the hard way, or easy way. Book the flight informing BA you have blind/visual issues, and you'll be travelling with your guide dog. Buy a hi-res coat for the dog and turn up at security then on to the gate. Not forgetting sun glasses and a white stick. The dog will then be allowed to travel with you in the cabin, as long as the dog is wearing the regulation harness, you'll have to sort that in the US.
Daz