My Fishy Australia

Question
Hi there,
I'm in dire need of an answer. I have a beautiful 10 month old Goldfish named Aussie, she is light pink in colour and about an inch and a bit long. Last week I decided it was time she got a filtered tank and a couple friends, as she is currently my only fish and she lived in a bowl. I know that more often then not fish need the top of the water broken, but goldfish do it on their own, and I bought more food and this TETRA tank in hopes that it would make her happier and give her ample amounts of oxygen. Additionally, I bought two new goldfish, from the same place I bought Aussie, as I always do when I buy fish, I told the clerk to give me the two most healthy ones, and to not make em' identical. So I read the instruction,let the tank equalize over night, and let the three fish get acquainted in the old bowl. They all seemed great in the new tank, but on the 2cd day the biggest of the two recently purchased fish was staying at the bottom while going to the bathroom. I left as guests were coming over, opened the door to my room (5 hrs later) and he was dead. Quickly, I removed the carcass so that Aussie and the small new fish would thrive. 2 days later (5 days in total of the purchases) the small new fish died. I thought okay; the fish tank they came out of was very grummy (they're feeder goldfish) so they may've had a difficult time going through the changes. Now, Aussie has been alone for 4 days, she is beginning to get deep red on all her "joints" if you will. Her tail, fins, gills, and it looks like its in the "vains" of her tail. I read an article here that states it may be the food. However, I'm concerned! Is it the other fish, the tank, the food, the filter? There are 1 million variables!!! Also I have cats, they watch the fish but cannot physically reach them anymore, (in the bowl they could but only Aussie... that one night we locked them in the other room). I'm extraordinarily puzzled! At 15, I can't quite understand weather they're stressed (If fish can be) or what!?! All I know is I don't want Aussie to be sick, lonely, dead, stressed or anything negative. I'm thinking its not ick as I am putting intensive research in on that. So, please, PLEASE, help me and my sweet fish. I love her very much, and I hope to be a Marine Biologist one day and she is helping me in many ways with that. Well, thank-you for reading this. If you can be of assistance in any way please send me back!

Once again thank-you, I understand if you cannot reply, but please try.
Sincerely,
-MLB

Answer
Hi There,

Your tank is still in the cycling process.
"Cycling the tank" means that you are establishing a bacteria bed in your biological filter to remove the toxins that the fish's metabolism creates. There are right and wrong ways to do this, and several things you can do to slow this process (which you don't want to do). There are two steps to cycling, but you don't have to do anything special for either of them. First, your filter will grow a culture of bacteria that digest ammonia and turn it into Nitrite (which is more toxic than the ammonia in hard water or water with a higher pH), then your filter produces bacteria that digest Nitrite and turn it into relatively harmless Nitrate. However, Nitrate will contribute to loss of appetite and stress in your fish, as well as contributing to algae growth, so it is important to do regular small daily water changes to keep your tank in best condition.

The red streaks on the fishes fins sound like septicemia which is a result of high ammonia levels caused by an uncycled tank.
The best thing you can do is daily water changes of about 50%.
Test your water daily to keep track of the cycling process. This will usually tank around 6 weeks.

Hope this helps,
Chloe :)