Swollen battery in MacBook Air

Regardless of warranty, you need to stop using the device and take it in to have the battery replaced. A swollen battery will swell further and can, at best, cause damage to other parts and, at worst, explode. Neither is recommended.

So, you need to set up an appointment with someone authorized near wherever you are as soon as possible. At that time, you can try to sort out your warranty issues; although a computer warranty is worldwide, there may be restrictions. Did you buy it new/factory sealed from Costco? I would not have waited months to deal with the issue as it can become dangerous.

Well, that would be for an authorized service provider and/or Apple to determine. You can then ask - the normal step is to repair first (in this case: replace the battery); if you waited too long, other parts may be affected. The one year warranty for a computer is worldwide. Apple will not replace a computer if a repair will fix the problem.

Make sure you have your purchase receipt handy since you did not buy it from Apple - did you register your device at Apple (is it listed as a device under your Apple ID?)?

That's good, but have your purchase receipt anyway - just in case.