Ok. first calm down.
Babies require different care then adults. While the petco babies are adorable, many do not make it to adult hood because of poor care in the store. It is very likely that you will lose the baby.
1) Babies need an actual heater (not a heating pad). Their water needs to be at 82 degrees (warmer than adults). Heating pads cause uneven heating and heating too quickly in tanks. Heaters are not that expensive if you find them online. The Hydro heater is often recommended on here.
2) With a one gallon you need to daily 100% water changes. GET THE BABY OUT OF THE CUP HE CAME IN ASAP. the ammonia in that was is EXTREMELY HIGH. I know you are young and can't get a bigger tank BUT you do need one. Maybe ask your mom to buy you one as a present. Or explain to her that your fish will not live a healthy live inside that 1 gallon tank. 2.5 gallons (mean 1 fish for 2.5 gallons) is the minimum for both babies and adults. Daily 100% water changes will easily stress a baby out and most babies are VERY fragile. However, with a 1 gallon tank you NEED to do daily 100% to keep the ammonia down (and keep the growth stunting hormone down)
3) What other fish food do you have? babies can eat crush high quality pellets (like Omega One or New Life Spectrum pellets), frozen foods like blood worms, brine shrimp, daphnia. Do not feed your baby any flakes or freeze dried foods. Your baby cannot live on the frozen daphnia alone. So you need to pick up high quality pellets and some additional frozen or live food options (blood worms, brine shrimp, etc).
4) babies need to be fed many small meals. They should be fed around 3 times a day VERY small meals. one pellet at each meal.
Bottom line - babies are a HUGE commitment and should only be taken in by very experienced fish keepers who have the means and space to keep them healthy. They really should not be adopted by those who are young and do not have the means to take proper care of them.
I know you said you want to save your money for medicine and stuff, however do you realize that if you spend your money on a proper sized tank with an adjustable heater and keep up with water changes then your fish will not get sick. You are not taking care of fish, you are taking care of water. If the water in your tank is clean and is changed accordingly then you will almost never have health problems with your betta.
In addition - Whenever you buy a new fish, you need to have his tank set up with the water filled in it and heated to the right temperature (78-80 for adults and 82 for babies). You can never bring a fish home without a proper tank set up, if you don't you will just cause your fish even more stress. You also need to go STRAIGHT home to the tank after you buy the fish. Not going straight home to the tank will stress your betta out, especially if you leave them in a hot (or cold depending on the time of year) car for hours.
