Does vinegar neutralize the strongly basic compounds in cement?
If you look for Portland Cement safety issues, it is stated that cement is highly alkaline so it can cause alkaline burn and presumably since vinegar is acetic acid, it neutralises the alkaline effects of cement as tested here and the burns you suffered are probably related to alkaline burn. You can look at this article section 6.5 for some details on alkaline burns, which was suggested by @Cornelius or perhaps the mentioned chapter in this book (Harchelroad FP, Rottinghaus DM. Chemical burns. In: Tintinalli JE, Kelen GD, Stapczynski JS, Ma OJ, Cline DM, eds. Emergency Medicine: A Comprehensive Study Guide. 6th ed. New York, NY: McGraw-Hill; 2004: chap 200.).