my cat has developed a gulping reflex when she eats or purrs

My cat Apple has recently developed a problem when she eats or purrs she does a "gulping" reflex like "hiccups" in humans but with a pronounced moving forward of the head.

I took her to the vets and she examined her,she could only find a little tenderness around Apple's larynx when she touched her neck and it made her gulp.The vet suggested full blood checks to rule out inflammation or signs of a tumour (lots of white cells in the blood who indicate a problem) but all bloods came back normal (thankfully)

The vet suggested that the only way to find out what was going on would be to give her a full examination under anaesthetic and also take X-Ray and if there is a lump there to take a sample for histology.I am reluctant to let Apple go through all this but at the same time I'm worried if I don't and it turns out to be serious?

Any advice would be greatly appreciated

Thanks from catlady