Isn't there a form of jasmine that's evergreen? Honeysuckle, but quite a few varieties are considered to be undesirable invasives. Woodbine? It's vigorous, but I'm not sure where you would obtain a specific variety. You might be best pleased with one of the evergreen clematis varieties. I'd vote against ivy, since it can be very difficult to control.
It would help to know your planting zone, since quite a few plants will be deciduous in zone 6, but evergreen in zone 8!

Can we assume that by southern Alabama, you're near the coast? You could certainly grow Confederate Jasmine, though it will need some support. I'm guessing that you have Carolina Jessamine, judging by the yellow flowers. It will probably take off this year; you just haven't given it enough time.

You might also consider Creeping Fig (Ficus pumila), which you can see on solid surfaces all over the south.

Woodbine (Virginia creeper) is not evergreen.

I am in mobile.I have alot of fence to cover and was wanting something to cover quickly.But I want it to stay green year round.Thanks