I have gone to a chiropractor on a regular basis since I was a year old (I'm now 33). My mom took me because I had one leg shorter than the other and the medical doctors said my only option was to wear a lift in my shoe. My mom truly believed chiropractic care would help me and figured that, at worst, it wouldn't do anything for me. Luckily for me, she tried it and my legs are the same length.
I take both of my daughters to a chiropractor. Even given my prior experience with chiropractic, I was hesitant to take my children and didn't start until 6 months ago when they were 3 and 1 1/2 respectively. I am so grateful that I did. My oldest was having recurrent ear infections and pneumonia. She's been healthy for the last 5 months. My youngest wasn't having the same chronic health problems, but I started her anyway. She used to be a horrible, restless sleeper. She's sleeping great. The adjustments they receive are very gentle- it doesn't take much pressure to move their vertebrae back into the right place. I would be a little leary of a chiropractor that wants to take x-rays of your son. I know some who do take them of kids and some that don't. I am of the belief that in kids they really aren't necessary- the chiro can feel what's wrong. But if the chiro feels that things are out of place, s/he may want to see your child several times a week at first to get things back in place and staying there.
As for the eye problem, it most likely is due to a muscular problem. I've had my youngest at the eye doctor since 6 months because I thought she might have a lazy eye. The muscle may just need to develop more. The chiro care may help, though. The muscle isn't going to work right if it's not getting the right signals from the brain. Our nervous system runs down our spine, and if a vertebrae is out of place, it pinches off that nerve ending attached to it. If the chiro gets the vertebrae back in place, then the nerve can work at 100% and get the right messages to the muscles and other body parts that are affected by that nerve. The nerves attached to the C1 and C2 vertebrae (the top two vertebrae) affect most of the head area, including eyes, ears, sinuses, etc.
I would do the chiro care and continue to follow-up with the eye doctor. The two don't have to be mutually exclusive, but rather can work with each other to make sure the eye muscles are getting the right messages from the nervous system and getting stronger.
If your pediatrician actually gives you a referral to a chiropractor, please let me know. I have never met a doctor that believed in chiro care too. Hopefully your pediatrician will see the benefit and give you the referral. But if s/he doesn't, don't let that discourage you from taking your son to one. Best of luck to you and feel free to email me if you want to discuss this more.