I agree with everyone else's information provide to you so far. I will toss in that I had a friend whose son had the same eating issues without the pincer grasp issue that was resolved as soon as he started doing a dose of probiotics each day. Turns out he had a pretty serious imbalance of healthy and bad bacteria in his digestive tract causing severe reflux, resulting in the gagging. By the time he was three or four, it was serious because he was so self limiting on foods. So long story short, you could try giving your son some probiotics, either in powder form you get from Vitamin Cottage or Whole Foods, or in the DanActive yogurt drinks. My friend's doctor was not concerned either, and she found this solution on her own with her dad's help, but obviously their lives are much better now that her son can eat a variety of foods without gagging and eventually throwing up. She has said that he self limits his food on days they forget the probiotics.
The pincer grasp could be a sign of there being something more sensory or developmental. I took my two year old to the child find services for speech, and although they decided we needed to wait and watch for 4-6 months and reevaluate, they gave us strategies to try and we ended up not having to go back, as the issues resolved themselves. They can be really helpful.
Another thing not to rule out would be food allergies, as they can cause a strong aversion and self-protection mechanism to food.
You can see there are several possible explanations for your son's behavior. It could also be normal for him and he may just need a little extra time. In which case, you jsut have to be patient. You now have lots of possibilities to explore, but most importantly trust your instincts. Don't be afraid to ask questions of experts, but if their advice or solution seems questionable to you, get a 2nd or 3rd opinion. Good luck!
H.