I am looking for the name of an eighties movie about an unfortunately ugly (possibly deformed) red-headed teenager. Unfortunately, I can't remember much more than that. I know it is from the 80s, but can't remember who was in it or the name. Thanks in advance!

Well the only thing I can think of because you said deformed would be "MASK" with surprisinly Eric stoltz as Rocky and Cher as the mom. The son is a red head with a deformed face... here's a link Mask (1985) (http://www.imdb.com/title/tt0089560/)
And a picture:) Google Image Result for http://www.cinema.com/image_lib/8907_001.jpg (http://images.google.com/imgres?imgurl=http://www.cinema.com/image_lib/8907_001.jpg&imgrefurl=http://www.cinema.com/film/8907/mask/gallery/page_2.phtml&h=393&w=600&sz=25&hl=en&start=1&um=1&tbnid=FmOaapsokHuGWM:&tbnh=88&tbnw=135&prev=/images%3Fq%3Dmask%2B1985%26um%3D1%26hl%3Den%26rls% 3DRNWM,RNWM:2007-37,RNWM:en%26sa%3DG)

The only movie that I could think of with this description would be Mask. This is an EXCELLENT movie. The boy Rocky (played by Eric Stoltz) has Elephant Man syndrome (can't think of the exact name of the disease) and it is a very touching movie. I am not a real fan of Cher, but she was great in this movie. I cry every time that I see it. It is based on a true story.