I agree with others that this baby needs several investigations. If he had a modified barium swallow and
was placed on thickened milk I assume that he has been seen by a Speech Language Therapist.
The fact that he tolerates thickened milk but not solids raise questions around whether he is actually choking
on the food he wants to eat or whether he is hypersensitive to food passing over his tongue and that this is causing
him to gag. 
I have seen this in a group of babies all characterized by a history of reflux. They are reluctant to eat
solids, especially hate being fed spoon foods, will do much better on finger foods with them being in control and the gagging, i.e. the response of pushing food out of the mouth, will decrease as the tongue becomes less sensitive to whatever is passing over it.  Reflux seems to sensitize the whole system so if it remains untreated things are not
likely to improve. On top of this many parents will resort to forceful feeding resulting in further defensiveness around food.
The gagging is also distressful to parents and instead of pushing on they stop offering food. If this baby tries to chew he is obviously pushing food onto his molars/gums through tongue lateralization. He will need super soft melt in the mouth finger food, but working with an experienced health care professional knowledgeable about dysphagia will be essential. 
Loraine Hamm
SLT/IBCLC
New Zealand   

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