Has anyone gone through this process who can explain how it works?

I’d rather not sell my current home, but I also worry the housing bubble could pop at anytime. I don’t want to get stuck upside on my home. Also, I’m not entirely sure I could afford the new mortgage, should I do this. Likewise, if I sell, I’ve hit a wall on finding someone where new that could be large enough for my two boys and I, as well as being at or below my current mortgage payment now $1270. Any advice would be greatly appreciated.