Many plants won't bloom their first year after planting - if that vine looks huge to you now, you may be underestimating its potential size, that isn't huge for Gelsemium sempervirens. If you are fertilizing, consider a low-nitrogen fertilizer for best flowering - water as needed to keep the soil barely moist all through spring. Lime won't help the plant to flower, this vine should be fine in acidic to neutral soil and isn't dependent on alkaline ph.

Huge and getting huger by the day since I installed a drip water system. It will have a problem if it get too huge, it will be out of space. Maybe it get too much water? I have to make some adjustments to cut it off from the rest of the system.

Maybe things bloom differently for you on the west coast, but here, in the south, Carolina jasmine blooms in late winter and early spring. Mine will be completely covered with blooms at that time. In the fall, it will sometimes have a few sporadic blooms. You should expect it to get a lot bigger, maybe tripling what you show in the picture.
Jim

Here is a link that might be useful: Carolina Jasmine

I will have to keep it pruned down to a resonable level or dig it up and find another place for it, because it is not going to have that much room. I have a lemon tree and another vine growing there. That link says it does like a lot of water. I was thinking it needs to be dryer to bloom.

My Carolina Jessamine blooms in early spring. It's common for them to wait until their second season before blooming.

These things can get big if you let them but are easy to keep pruned.