Hard tea is a good way of describing what you have made. It's tea and sugar that is fermented with wine yeast. It's high alcohol, unlike things like Twisted Tea. So it's interesting, but not kombucha.
To make kombucha, you need tea, sugar, and a culture that's a mix of yeast and bacteria (calld a SCOBY - symbiotic culture of bacteria and yeast. It's symbiotic because the yeast and bacteria work together and need each other to make the environment good for both). You can buy a SCOBY or get one from someone, or you can use a bottle of kombucha that you buy from the store.
For a gallon batch, you need to make a gallon of tea and sweeten it with a cup of sugar. To that, add 2 cups of the "starter tea" (existing kombucha - comes with the SCOBY if you buy it, or use a bottle of commercial kombucha). Put your SCOBY on top and cover with a cloth secured with a rubber band. Note that you really only need 3.5 quarts of the sweet tea, but it's easier to make a gallon.
Ferment that for a week and then taste it to see if you like it. I like it after 2 weeks sometimes, when it is more tart.
If you follow my link, there are a couple of more detailed posts about my process. Getting the kombucha SCOBY and starter tea is essential.
Again, sounds like you make high alcohol hard tea, which sounds good, too!