Is mild burning on one side of throat not related to swallowing for three months worrisome for throat cancer?

Not necessarily: That kind of symptom could be as simple as post-nasal drip or acid reflux but you should definitely have it evaluated further since it has been consistent and is not normal.

Get checked: Anything that lasts for this long should be evaluated by a health care professional. Yes you could have throat cancer, but many other things might cause this. Please see your doctor.

Could be: It could be from different things like chronic inflammation, trauma, cancer etc. Dont delay anymore- you should see an ENT for direct visualization/examination on your throat. If there is anything suspicious, a biopsy will need to be done.