Thanks for the post. If by cycling you mean "did I leave the tank to settle for 4 to 6 weeks?" then yes I did that.
"Cycling" refers to the nitrogen cycle that oxidizes toxic ammonia released through your fish's gills and by decaying matter like fish food to nitrite and then nitrate, both of which are non-toxic in saltwater tanks.
To start the nitrogen cycle people usually provide an ammonia source that allows the required bacteria to start working. If you just let the tank settle without adding anything to it it's possible there weren't many nutrients to work with leaving a fairly weak nitrogen cycle, but it might be fine.
You already were advised to increase salinity ("sg") very slowly but to be sure your measurements aren't off I would be interested in the exact measurement device you are using and (if it's a digital salinity meter or a refractometer) how it was calibrated.
Another very important aspect is oxygen. Not only is it required for your fish to breathe but also for important bacteria that keep the nitrogen cycle going. Do you have a protein skimmer running or at least some air pump connected to the tank?
Sooner or later you will need to make your own saltwater if your local fish store doesn't sell saltwater with an appropriate salinity/sg. I recommend getting an appropriate salt for reef tank use. Instant Ocean is one of the more affordable options and has a good reputation, but you can also get a different brand like Tropic Marin, Nyos, etc.
It is very likely that you can't use your tap water for mixing saltwater or topping off evaporated water, so you will need to buy "RO/DI" (Reverse osmosis/ deionized) water from your local fish store or get your own RO/DI filtration system which is a whole topic that requires proper instructions on its own.
All this is a lot for a beginner so the most important parts will be:
- Oxygenation of the water with a protein skimmer or ar least air pump, and water movement with flow pumps/gyres.
- Double checking the salinity reading so you don't accidentally increase salinity even though it's already correct or even elevated.
If those two are in order your next step should be to see what your fish actually has. Time is certainly a factor here as the fish isn't eating, but without Oxygen and under the assumption the salinity might be a measurement error the fish's behavior might be explainable just from these factors.
