I have also skyrim underwater issue but mine looks diffrent... i don't have green screen... i have grey... but i heard that it is the "enb mod" from 1.5 update of skyrim that causes the problem.. however i do not know how to fix it.
But I found this mod:
OpticShooter's WATER mod, it fixes all underwater problems, however not everywhere i think.
Another thing I saw that is possible to do to fix the issue is actually to write in the console (pc) "tws", which actually toggles water on/off. Aswell another possible console command able to use to fix it is the "tcl" command, which toggles collision on/off.
However there are things you should know about these commands before use them.
Which can be found here:
Skyrim Console Commands
EDIT: Also found this for you who has problem with the green underwater screen problem, here's a fix for it:
Green underwater fix