Hi again. Good--you changed the water. As for the white specks on his tail he could have a condition known as Ick. Ick are small little parasites that latch onto a fish causing a fish to look as if it had salt spread on it. So I recommend using a medicine to treat the Ick.
You can buy Rid-Ich+, Ick-Attack or just about any Ick medicine that's available in your local pet shop. Just follow the directions on the product label. With regards to tank size--yes it would be better for him to have at least a 5 gallon tank if not a 10 but I really understand that sometimes money becomes an issue with fish products and sometimes we just don't have the finances at the moment to buy what's ideal. So for now, change his water ideally every other day.
If not at least every 3rd or fourth day. Remember this goldfish's excretion stays in the tank until you change the water. If the water's not changed regularly the excretion builds up thereby polluting the water. So to sum things up, 1)treat with Ick medication, 2) change the water frequently and remember to use a dechlorinator (something that takes the chlorine and chloramine out of the water) and 3) look into a bigger tank.
Hope everything works out well quickly and let me know if you need further clarification on what I've written above. Also feel free to contact me with further questions. Thank you for submitting your question.