Eyelashes do grow back. I would recommend that you seek the care of an eyeMD to determine the cause of your itchiness and throbbing and obtain appropriate treatment.
Dr. Feldman,
Sandy T. Feldman, M.D., M.S.
ClearView Eye and Laser Medical Center
San Diego, California
Usually they will grow back, provided you are in good health with no metabolic or systemic diseases and you have good eyelid health. Please see an ophthalmologist to see about the eye and eyelid irritation. I can't give direct treatment advise for you since I am not your doctor.
MJK MD