Wow. I think your mother is mistaken or perhaps performed a switcharoo on you. >_> The fish looks like a marble, and usually marbles go solid or marble out when they mature.. But that is beside the point. You must do a 100% water change.
This means putting your fish into an alternative container, such as a cup or tupperware container. Make sure that the cup is clean, and is in a safe place where it will not be knocked over, and put something over it so that the fish cannot jump out. Next, you need to take your tank to the sink and pour out all the water, make sure that you pour the water into a strainer or a colander if there is gravel in the tank--you don't want any of the gravel to go down the drain. Rinse the tank and everything in it with hot tap water so that you get all of the uneaten food, poop, and ammonia residue out of the tank. Then put everything back in and fill the tank up with water that is the same temperature as the old water you took the fish out of--you might want to keep a sample of the old water next to the sink. Dip your hand from the old water to the faucet, adjusting the temperature as necessary until they feel like they're the same temperature, then fill up the tank. Depending on how heavy the tank is, you might want to only fill it partially, put it back on the stand, and then use cups to fill the tank back up if it is too heavy to move. Next, add dechlorinator. Give the tank a good stir and then you can start acclimating your fish to the new water.
To acclimate your fish, float the tupperware/cup/bag that he is in in the tank. Every few minutes, pour out some of the water from his container, and let in some of the new water. Do this very slowly and carefully
--since the water he was in previously was so dirty and awful, you should acclimate him over the course of an hour.
In the future, you should keep doing water changes regularly. If the tank is one gallon, he will need a 100% change like this every other day. If it is two gallons, every two to three days; 3 gallons, four to five days; 5 gallons, once a week. Since, after this water change, the water parameters will be much more similar to any water you change the tank with in the future, you will only need to acclimate him for 15-20 minutes instead of an hour.
The fish also looks emaciated.. how much/how often and what have you been feeding him?
When you go buy your heater, look around for some pure methylene blue. Methylene blue is a very gentle chemical that will help your fish recover from ammonia poisoning and will help prevent secondary infections--it is a more effective preventative than salt. Also, when you get your heater, look for one with an adjustable temperature dial, like this one: http://www.fosterandsmithaquatics.co...8&pcatid=11368
Mini heaters, pre-set heaters, and heater pads are poor quality products that will underheat or overheat the water based on the ambient temperature of the room. For instance, if the room is 68-72 degrees, it won't heat the water enough, and if the room is 80 degrees, it will overheat it. Adjustable heaters are a few dollars more, but the security, stability, and control they offer you is well worth the investment. I encourage you to shop online, you will get a much better price and more variety to choose from. Even with shipping added in, the prices are much more reasonable than what you will find in any retail store.
Remember, when you put your heater in, adjust the setting so that it matches the temperature of the room, and slowly adjust the heater up a degree every couple hours. This way you will avoid shocking your fish.
Please read this article when you get the chance, if you have not already: http://www.bettafish.com/showthread.php?t=49160