Thank you for writing!
For public lice, there are over-the-counter medications available in the form of 1% permethrin. A mousse containing pyrethrins and piperonyl butoxide can also be used.
Permethrin is used to treat scabies, as you mentioned, at a 5% dosage. Be sure to read the instructions carefully and follow suit.
If you don't see improvement within a few days, contact your doctor.
You will also need to clean you house, bedding, towels, blankets, sofa coverings etc, just as you would with regular lice. Wait for total clearance before engaging in sexual activity again.