That's so sad that your nephew died so young. How tragic for your family. Lots of prayers headed your and your sister's way.
An ear-nose-throat doctor is your best bet for the throat tickle. Tell them what you're experiencing, and they'll be able to check you out for most of the things your sister mentioned. To check out your larynx and trachea to make sure your breathing passages are fine, they may do a laryngoscopy, in which they pass a camera at the end of a small, flexible tube up your nostril and then it turns to look directly down your throat. I've had this done twice, and it's a simple procedure. They will numb your nostril with some sort of agent, and then you won't feel the tube much at all. ENT docs are also the ones who usually attend to allergies.
I know little about esophageal cancer, except what I've learned through having acid reflux, but I believe there are many more symptoms to that than just the throat tickle. A gastroenterologist would be the person to consult about that.
I expect you'll be just fine, but as a health anxiety sufferer myself, I live by the better safe than sorry rule. And the doctors are the folks who would know best.
Good luck, and let us know what you find out.
Hugs and prayers,