An Education visa for yourself is around 50k a year. Your child should be at nursery and this way they might be able to get your the documents to do an education visa for your child too
Get to an agent asap. Let them handle the overstay and they can get a 30 day extension if that possible or do a visa run. One or the other. Cambodia visa run or Lao depending on nationality
When I did it. She had a letter from her employer stating she was granted 3 weeks from work with the start and ending dates of her 3 weeks holiday. This was to make sure she came back to Thailand to work. It was granted just because of the letter from her employer. It only took 10 days. But that in 2020.