Learning the Thai months is a bit tougher than learning the days of the week, but you’re going to need to know them at some point. I learned a few of the months as they came up during my life (birthday, travel, etc). Later, I got a calendar and made a point to gradually learn the rest of the months over time. I’d look at the calendar every day and try to write out the day at least once a day for the entire month. It took a while, but it worked.
Hopefully, you can get them into your head faster than I did.
If you have trouble remembering the months, connect them to dates that happen within those months. For example, “My birthday is in ___.”, “Christmas is in December.”.