Feeding Goldfish For Fall

Hi.We have a goldfish problem and I was looking for some help. My Son won Goldy at a Church’s Fall Festival Saturday. We told him it was really cold that night, but if it was still alive the next day, we would get him a tank and food. He is a little thing and didn’t move around much in the plastic bag he came in. He was alive Sunday so we went to local store and bought an aquarium kit, gravel, fake plant and Wardley Goldfish flake food (because it said helps maintain clean water). We rinsed out the tank, rinsed the gravel, added the rest and let it run for 24 hours till we added Goldy. Monday when we added him/her, there was feeces trailing from body. I didn’t know what it was, so I started looking online.I read about constipation, but I figured the poor things been kept in a bag for no telling how long, so I figured no wonder its constipiated, and that now it had a wonderful tank and food so it would be doing better real soon. Goldy looked healthy otherwize to me, but he stays at the bottom corner of tank alot. I thought he had white-ish spots on tail and body, but I don’t know if it his coloring or something else.He is fed 2 times a day with just a little flake or 2, but he dosent seem too interested in the food very much. Thursday we added the aquarium light (it had been missing from the kit) and a ceramic sign from the fish dept (rinsed it off first). I did see him eat a bubble or two, but not that often, he still stays at bottom mostly. Friday, noticed part of his tail was gone! Looked online, think it is tailfin rot, sent husband to store again. Only thing that had for it was fungus clear tank buddies tablets for 10 gal tanks. Because our tank is smaller, we broke tab and added part of tab. Today, his little tailfin has blood red streaks. I don’t know if that is good or not. I don’t know if it is new blood to the area to regrow tail, or did the medicine hurt him? I have now been reading about goldfish care, and it seems like we are doing everything wrong, when I thought we were doing everything soo good for Goldy. Our tank is one gallon with an “undergravel filter system” and air pump with diffuser stone and above light in hood. I though this would be so much better that just a fishbowl, but I am reading that I needed a 10 gallon tank for one fish!!!!! and that an undergravel filter system is not very good 🙁 . I had even promised my Daughter that if Goldy did good, I would get her a goldfish to add to the tank! I once took care of my Grandmothers Betta fish for months when she was sick, and the only thing you did was drop pellet into straw and change water once a week, and it didn’t even have a tank, just the glass vase! I though a goldfish were hardy, easy care and inexpensive. This is my 8 year old Son’s first pet, and I would like to do our best to take care of it. We live in a smalltown and there is just one superstore, and no fish stores. I would like advice on what we could do that is inexpensive and that we have access to. I am feeling foolish that I thought it would be so easy. I hope you have some advice. Thank you,
CurrenMom

I took out about 1/2 the old water and added new water (that had been sitting out for days). I then added some more of the fungus clear tab. He seems to be moving around alot more, he used to stay at the bottom corner alot. But I noticed he sure is moving his mouth alot and I might be seeing black spots…