It is possible to keep a fish in a gallon bowl, but it is much harder than im a larger container because it is so small that the slightest thing can throw the temperature or chemestry off. Also it is hard putting aquarium accessories in there, even if they are scaled to the bowl. ;)

I have used bowls for sorting fry and quarantining or at least holding new acquisitions. Almost all the time, water is partially changed as often as I can. Most, let's say 70% of that water is from an established tank, which is reasonably clean. The other 30% has sat for a week or three in a food quality holding barrel. (Our water supply has chlorine, which will dissipate over that time. We are fortunate in that our water department does not also add ammonia to te chlorine, because that water is much dangerous if untreated.) I try really hard to make sure that the water chemistry and temperature is pretty much the same for the bowl and new water.

Red spots, sometimes called "fingerprints"
of Aeromonas bacteria, can be the beginning of tailrot. Keep up the partial water changes. It might be possible to add an antibiotic, scaling the dosage to one gallon, but i would suggest instead changing 1/3 of the water a day, if you can "season" it for a few days before the water changes. (On your scale, are you keeping a few open gallon jugs with tap water sitting in them?) You don't want to take all of the water out if that is you only fish home, because you can pretty badly set back or destroy the nitrogen cycle.

If I'm confusing you with phrases like seasoning water, partial water changes and nitrogen cycle, you need to Google those phrases or Google {Guppylog and ... each term}. These are necessary parts of keeping any fish, whether it is a mollie in a bowl or a shark in a 100,000 gallon tank.

Also, look around the house and if there is a place for a 10-gallon aquarium. They are 12" high by 20" by 10". A so-called 20 gallon aquarium is even better, if you can afford the space and cost. That tank will still have to be cycled. You will still need to do partial water changes with seasoned water. A filter (a box filter will do fine) and a thermostatic heater is very important. But your mollies will stand a much better chance of living comfortable and full lives.