A UV sterilizer will eliminate/kill free floating algae.
Until you find the underlying problem, though, it will always come back once you stop using UV.
Something is causing the bloom and finding out what it is will be best in the long run.
If you want to use a UV sterilizer to get the problem under control, it should work like your LFS says. I'd look online for one, though, as it will probably be much cheaper.