, just one thing before the visa expires you apply for a visa extension based on marriage, from your local immigration office, this requires more admin, like financial proof etc, give yourself time to understand the requirement, so it goes smoothly. I visited my office with my Thai wife which helped a lot, as each office can have a different view of what's needed.
If you only have a ticket to Thailand and need a visa, the airline will not let you fly.
If you have two tickets Bangok/Yagon you can transit through Bangkok airside (without going through customs) if you are not issued a second boarding pass in Shanghai there will be ticket desk in transit where can get it.
Check carefully your requirements for Yangon, its not the easiest country to get into.
As regards your luggage I'm not sure, but suspect there will be a place to stow at the airport.