OK- You've gotten alot of conflicting info here!
Here is my experience - also with my first, so I felt CLUELESS! He started resisting foods at a year old - didn't like "chunks" of anything in his food. He mainly started only liking his milk (switched from breastmilk/formula to whole milk at a year, but he would only drink it with Ovaltine mixed in and warmed! LOL!), he loved CHEESE, and all other dairy products. He liked only a few fruits, and even fewer veggies. He started the constipation around a year or so - SCREAMING in pain after 3-4 days of not having a BM. I tried all kinds of stuff - although not as many as have been suggested here! {I wish Mamasource had been around 10-12 years ago!} Part of our problem, other than all the dairy he ate, ended up being too much iron! He also loved meats and I gave him vitamin drops in his milk, that had ADDED IRON! Duh! So between those two things, his body became accustomed to the constipation and he associated BMs with PAIN, so he would hold it in! I had to help him out with Qtips several times! Suppositories usually just came right back out w/o helping. We also used some kind of children's laxative that was OTC at the time (Senokot maybe?) but I didn't like programming his body to only poop with drugs!
When he was 4, and at the end of a painful BM (which happened less and less by then, but still happened!), he actually pushed OUT his rectum - the doctor called it prolapsing... I totally freaked! I had to push it back inside of him - horrible for both of us - but mainly me, it ended up not hurting him that much, but he had a constant feeling that he had to go poop for a few days aferward. Since then, we've managed to find a few veggies and fruits he will eat. When he was 5 or 6, my MIL introduced him to fresh Spinach leaves in salad, as he would not eat the white or light green lettuce I'd always had in my salads. I was never much of a spinach eater, but started mixing it into salads for his sake. He is 12 now and still picky, but goes to the bathroom almost every day, and most of it I think is due to his daily does of Frosted Mini-Wheats! He tried several high fiber cereals - we could even give him All Bran for a while as long as there were bananas or berries in it. Awful to me! And he stopped liking it so much, but has always loved the Shredded Wheats.
Hang in there, and try whatever you feel will work for him. Some of these suggestions have TONS of sugar, which always makes things worse, and yogurt, even if it does have probiotics, is DAIRY and is used to help with diarrhea, not constipation. Plus the sugar content...
Another note - my second son had the complete OPPOSITE problem - 7-8 runny dirty diapers a day!!!! Toddler diarrhea with him! He ate everything under the sun!!!
Hope you and your son find some relief soon!
A.