Hi and welcome. What test kit are you using? Strips aren't very accurate, a liquid kit is best (API Master kit).
Unfortunately you didn't properly cycle the tank first. Cycling means growing the proper bacteria in your filters to consume the ammonia your fish put out; the ammonia is then converted to nitrite and then nitrate. In a fully cycled tank you'll never see ammonia or nitrite on the test (unless somethign is wrong), and nitrates would be controlled through weekly water changes. This process can take 1-3 months on average.
Products like stability are every unreliable. Most don't contain the correct bacteria and of those that do it's very hard keeping bacteria viable that's sitting in a bottle on the shelf.
How long after you got fish did nitrites rise? Testing your tap water for ammonia, nitrite, and nitrate isa good idea too so you know what you're starting with. Did you check for ammonia as well?
What kind of fish did you get? Overstocking too fast could be an issue too.
Since you have fish you're in a fish-in cycle. I'd stop adding the stability. What are you using for dechlorinator? Prime is best if you can get it but whatever you have on-hand is fine.
With nitrite that high you're going to have to do some serious water changes to get them down, probably multiple back-to-back 60-70% water changes over a couple of days.
Once nitrites are down, you want to test the water daily for ammonia and nitrite and nitrate. Any time ammonia and/or nitrite are over .25, do water change(s) to get them down.
Of course this is assuming the tank isn't overstocked. If you have too many fish or inappropriate fish for a 10 gal
it'll be tougher to keep on top of water changes to keep the levels down.
There's a link below in my signature: new tank with fish. It's a fish-in cycle guide that'll help. You might also want to check out the "guide to starting a FW
Hope this helps.