Stangier, U., Ehlers, A., & Gieler, U. (2003). Measuring adjustment to chronic skin disorders: validation of a self-report measure. Psychological assessment, 15(4), 532.
http://www.researchgate.net/publication/8944324
A lot of papers are specific to certain diagnoses.
This discusses several measures, but includes 'Questionnaire on Experience with Skin Complaints' and also 'Dermatology Life Quality Index' (DLQI) mentioned above by Prasanth.
Bhosle, M. J., Kulkarni, A., Feldman, S. R., & Balkrishnan, R. (2006). Quality of life in patients with psoriasis. Health Qual Life Outcomes, 4(1), 35-37.
http://www.hqlo.com/content/4/1/35#B32
This was the original paper reporting DLQI:
Finlay, A. Y., & Khan, G. (1994). Dermatology Life Quality Index (DLQI)—a simple practical measure for routine clinical use. Clinical and experimental dermatology, 19(3), 210-216.
This paper mentions the 'Questionnaire on Experience with Skin Complaints' traces it back to the original format of ‘Feelings of Stigmatization Questionnaire’ (Gingsberg & Link):
Schmid-Ott, G., Kunsebeck, H. W., Jager, B., Sittig, U., Hofste, N., Ott, R., ... & Lamprecht, F. (2005). Significance of the stigmatization experience of psoriasis patients: a 1-year follow-up of the illness and its psychosocial consequences in men and women. Acta dermato-venereologica, 85(1), 27-32.
http://www.researchgate.net/publication/7888736
This is their reference for ‘Feelings of Stigmatization Questionnaire’:
Ginsburg IH, Link BG. Feelings of stigmatization in patients with psoriasis. J Am Acad Dermatol 1989; 20: 53–63.
http://www.ncbi.nlm.nih.gov/pubmed/2913081
These papers also gives some suggestions about measures:
Marshall, C.& Bewley, A. (2015) Psychological care: Quality of life assessment in skin disease.