Would silent reflux cause swelling in the throat and cause trouble eating solid foods? if so what tests would show swelling in the throat area?

Yes it can be reflux: GE reflux is a common cause of feeling a swelling in the throat and trouble swallowing. Often it is accompanied by hoarseness, especially after eating. There are a few tests that can determine this. An ear, nose and throat doctor can look at your throat to see if your vocal cords look swollen. You could also do a barium swallow. You could also try an anti-acid med for a month to see if it helps.