The British Hospital is great. The doctors there were the best students in medical school. When the students graduate, they want to go to work to the British Hospital. Besides, the atmosphere is really nice and comfortable.
You need a dermatologist. There are MANY in Buenos Aires. If you want to go through a private clinic you can try the British Hospital or a better one such as the IADT (Instituto Argentino de Diagnostico y Tratamiento). There are many posts in this website about medical care in the city.
Dr Fernando Stengel is also one of the best and speaks english as he worked years in New York. i think his clinic is called Buenos Aires Skin and on Cordoba at Libertad. if you can't find, PM me and I will dig up number.
There is a derm clininc in Uriburu 1590. The head doctor there is Dr. Chouela, but you can see anyone of them. tHey have the latest technology and very good specialists. www.chouela.com 4805.7485. Good luck!
I went to Buenos Aires Skin and saw Dr Politi for a few suspicious sun spots. Professional, knowledgeable and made sure I understood everything. Recommended.