If food is getting stuck frequently mostly it would be either what you are eating or how u are eating it, everyone is different. Some cannot eat quickly, some cannot eat certain foods, some cannot drink with food, some find mornings their band is 'tighter', what you have to do is monitor what you eat and how u eat it, if food gets stuck then try eating slower, chewing more or avoid that food again, what u shouldnt be doing is throwing up daily. As the previous poster AnnieM says watch out for too much vomiting as this can sometimes cause problems with your band.
I was banded in Jan 2011 and maybe have thrown up 15 times since then at most, i am reliant on my memory, as what makes me sick doesnt get eaten again unless i can see another cause like i was very hungry and just ate too fast or didnt chew my food enough. My best friend is a sharp knife i cut up all my food really small, i do not eat bread or bread products at all, and tend to avoid things like cold chicken as that is a big no no for me. What i do eat a lot of is Soup, homemade vegetable soup or tomato soup from weight watchers. If you do throw up then give your band /stomach time to recover, going onto liquids/soft food for the rest of the day is good advice. Eventually you get to know your band and what u can and cant do with it, i had to change my whole approach to food and what i was able to eat where other people just ate smaller portions of 'normal' food. Food can get stuck more often after a band fill so be cautious after a fill for a few days and hopefully things will improve.
I really hope you find the answers that will help you , the information here on this forum is very helpful. I have lost over 120lbs so far so be patient and i really hope things improve for you .