You have to clay & polish before you do anything, especially on black. You can even do everything by hand if you dont have the tools. Wax would be the last step in the process. I'm certain you still have oxidation, & other grime under that wax. Never gonna get it smooth the may you're going about it, or remove any swirlies. My finish feels like a baby's ass right now, & better than new.
Wax will last maybe a month or two with regular washing, while sealant can last you at the least 6 months. I dont wash much since I use a duster, & good Zaino soap that doesnt strip the coatings.