Hello and welcome. We appreciate your question on the forum. We're glad you are working with your doctor and urge you to continue to do so. That's the best source of information. Your doctor doesn't appear overly concerned. That probably feels a little annoying but at the same time, should be a bit reassuring. Having one tonsil bigger than the other is not uncommon. And if you were sick and there was swelling, it would cause the sensation you are experiencing. Is the sensation of feeling like something is in your throat gotten any better since you took antibiotics? Does ibuprofen with the property of reducing swelling help?
I would seek out the help of a specialist called and Ear, Nose and Throat Doctor (ENT or an otolaryngologist. This type of doctor is best suited for helping you.
This could be a tonsil/throat stone. https://www.webmd.com/oral-health/guide/tonsil-stones-tonsilloliths-treatment-and-prevention#1. A doctor who specializes in throats could look at this right away and know most likely. The sensation of difficulty swallowing or something in your throat is a common
Another common health issue that causes something to feel caught in someone's throat is acid reflux or gerd. https://www.medhelp.org/posts/GERD-Acid-Reflux/Something-stuck-in-throat-feeling/show/1360181
As to tonsil cancer, that is always something that provokes anxiety to worry if what we are dealing with is cancer. Please know that the likelihood for you is not. First of all, tonsil cancer is most prevalent in men. It's also most common in those over the age of 50. Those statistics don't mean it couldn't happen to you but the chances are much lower. Here is some information on tonsil cancer: https://www.mayoclinic.org/diseases-conditions/tonsil-cancer/symptoms-causes/syc-20367939. Very true that the number one symptom is feeling like there is something in the throat or difficulty swallowing. They can use a lighted instrument that will show if there are abnormal cells on your tonsil to decide if further investigation is needed. Again, an Ear, Nose and Throat doctor is well suited for this.
Let us know how you are doing and if going to an ENT is possible for you.