Stay away from Clobber, Blast Out or any of those professional drain cleaners that contain sulfuric acid. If the fumes get inside the house they can scar your lungs. I know, my lungs are scared from using muriatic acid in my fathers shop when I was a boy. I am no fan of putting harsh chemicals down your drainage system especially if you have a septic tank.
I'll hang in there with you when you snake out the line and walk you through it if you wish. Regards, Tom