Sounds as if he is eating too much solid food, sorry. Just because he wants it doesn't mean it's best for him, no offense to your doctor.
The constipation seems to be a major sign of this, as well as the spitting up, he's stuffed. To eat as much as he is in just 2 weeks of eating solids is a LOT! Usually at the beginning they eat a few spoonfuls and no more than half a jar at a time. Offering them one food at a time for a few days is the best way to get them to like that particular food and see if there are any sensitivities to it. At this point you couldn't know if he has an allergy to anything, unless he only spits up after eating that particular food. And, I'd definitely cut out the bananas as they are a constipating food, and switch to prunes.
Your breast milk actually offers the majority of nutrients he needs, eating solids at this age should be to introduce them to the concept of eating food and moving it around in their mouth and swallowing, rather than just sucking and swallowing, not to have it sustain him. Always nurse him prior to his eating, offer him cereal (usually the first food offered) mixed with breast milk, and gradually introduce some fruit into it. Also try giving him water at this point, in a bottle or sippy cup if he's ready. Breast milk offers enough water on it's own, but the additional fiber of food needs water to go through his intestines, otherwise you get the constipation.
One last tip, make sure he's getting time to move and crawl around, you can help by moving his arms and legs like he's riding a bicycle, as the exercise will help get things moving through his system.
Mom to 3, Grandma to 7 : )