get. some. rock. Seriously, it i s not just for decoration like in a fw tank. Live rock is, like Greech said earlier, a vital part of the actual biological filtration in a sw tank. Meaning that's what you need to bring down those inexplicably bad chem numbers.
you can start with "dead" rock since it's way cheaper, but get at least a few pieces of the live stuff since the life in them will spread and enliven the dead ones. And the sand. If possible I would suggest you take the damsel back to the store or wherever you got it. Yeah I know it's surviving but "off the charts" ammonia and nitrite is just cruel. Some livestock will help the cycling process along but stick to snails and some hermit crabs and such.
I meant to ask you in the beginning why you were avoiding live rock but figured hey, it's your tank, none of my business. But this time you asked what you could do so well, there you are.
A month is on the one hand not long to be cycling a tank that size. But on the other if you had live rock it might nearly BE cycled by now at least to where you could maintain a damsel just with water changes. My 10g first salt tank will be all of 3 months old tomorrow and it's been supporting 2 clowns, a cleaner/skunk shrimp, 2 turbo snails and 3 hermits for 1 month. But the first month was nothing at all until the ammo/nitrite numbers came down. Going to change a couple gallons tomorrow but that's just on general principles, not because the tests are showing any need. The live rock sustains, it really does.