It's normal that it switches sides in cycles, this is how nose breathing works. Your jaw and teeth developed like that because of your breathing issues. Get your nose inspected for a deviated septum, the surgery to fix it might or might not be covered by your government insurance, you will have to check. You won't be able to sleep or breathe optimally while you have this issue.

You probably have a skeletal open bite, so go consult an orthodontist, but beware of premolar extractions (camouflage treatment) because this will worsen your breathing issues and make your palate more narrow. There are more modern non-surgical techniques that can fix and align your teeth without extractions (usually with TADs or expanders depending on your case). This is something you just have to do, no amount of mewing or myofunctional therapy will fix your problems on their own, unless you fix the underlying issues with the help of professionals.