How serious are your girl's ammonia wounds? If they aren't too bad, just aquarium salt should be okay. The triple whammy right now might be too much. Put her in a hospital tank too, if you can. With aquarium salts and/or meds, it's best to change the water completely every day and you'll find it's soooo much easier to do in a small tank. Once she's better, you can move her back to her side of the 10g and resume cycling.
Do you have an ammonia test kit? When you're just starting out with a new tank and you're cycling it with fish, it's a godsend to have. Test the water every day to monitor the ammonia and when it gets over .25, do an immediate water change, about 50-70%. Keep testing and changing the water any time it gets over .25. Eventually, you'll find that the ammonia levels drop and the nitrite levels rise as the bacteria establishes itself. At this point, a nitrite test kit, or better, a whole master kit or test strip, will help. Test for the nitrites every day and again, if they get over the safe zone of your test strip/kit, do a water change. Repeat every day until you see the nitrite level drop and the nitrate level rise. Change the water as always and keep testing to monitor the levels. Once ammonia and nitrite stabilize at 0, your tank is cycled and all you have to do is watch for high nitrate levels.
Or, if you simply don't want to deal with any of this testing, then the best thing you can do is change 50% of the water every week. The tank will still cycle, just very slowly. The main thing is to stay on top of the water changes and not overload the biofilter with too many additions at once.
I hope both your bettas recover soon and get back to happy swimming.