Which is the closest star after our own Sol?

Proxima Centauri, the Alpha Centauri A and then B, followed by Barnard's Star

Think it's alpha centauri but im not certain.

Alpha Centauri A - 4.3 light years.

I guess technically Alpha Centauri B and Proxima Centauri are the same distance.

Proxima Centauri is technically the closest. It's part of the Alpha Centauri trinary star system.

https://imagine.gsfc.nasa.gov/features/cosmic/nearest_star_info.html

any of the centauris

Proxima Centauri...which might well be why it is so-named... ;)

But the $\alpha$ Cen system as a whole is closest, and happens to have 2 other stars besides Proxima...