Yes, these are definately Balloon Mollies. I never actually owned them myself, but I did debate getting a few in the past because they are excellent fish to put in a tank with
goldfish. I decided to get a few Peppered Mollies instead, but I have no doubt those are Balloon Mollies.
Congrats on the babies! My Peppered Molly female had babies, but most didn't make it because I wasn't expecting them. She didn't look pregnant fat, but just kinda fat in general, so it was sad for me, but I'm soo happy to hear you have babies!