It's definitely related to using Fix-A-Flat. The Fix-A-Flat has added enough weight to the inside of the tire to throw off balance.
Unfortunately, the fluid it puts inside the tire will likely continue to keep that tire unbalanced, even if it is rebalanced at a shop. They may even find they are unable to balance it because when it's on the machine, since the weight inside (the liquid) keeps moving around, it will be impossible to "zero" the weight of the tire and achieve a smooth ride. The good news is that you likely do NOT need an axle replacement - the unbalanced tire won't cause that to fail.
The proper solution here is to either have the tire professionally patched (which would include also unmounting the tire from the rim and cleaning out the Fix-A-Flat "gunk"), or replacing the tire. Fix-A-Flat isn't intended to be a permanent fix for a leaking tire.