Couple questions to start with:
Can you share your complete water test with us?
What filter do you have and how long have you had it?
When adding water, do you add prime or other conditioner?
Are you able to get a picture of your fish to post?
Here is a good article to read if you have not read it yet about cycling:
I just learned about cycling but I already have fish. What now?! - Aquarium Advice
And a post with links to other articles to look through:
Articles to Help you Get Started with your Aquarium
Just a quick analysis: your new tank doesn't seem to be cycled yet. Test the water daily until the ammonia and nitrite reads 0. After testing, do a 30-50% water change.
With goldfish though, you should only keep the one in a 10g (and a 10g is too small for goldfish). Recommended tank size that I see regularly for goldfish is 30g. In the forum list, there is a coldwater forum under the Freshwater section. There is lots of good information there also.
Anyone else have something to add/help?