I've been using vinegar rinses once or twice a month for the last 40 years with no drying or damage of any sort. I use whatever vinegar I want to use up - cider, white, rice, etc.
I've never tried baking soda only because I don't have a need for it. Conditioner, gel, honey and vinegar are all I really need to keep my hair happy.

If I was having a reaction like you are, I would give both of them up, do a deep treatment, and then if I wanted to try them again I would do one at a time to see how my hair reacts.
--I'm located in Western PA.
--I found NC in late 2004, CG since 2-2005, started going grey in late 2005.
--My hair is 3B with some 3A, texture-medium/fine, porosity-normal except for the ends which are porous, elasticity-normal.
--My long time favorite products are Suave & VO5 conditioners, LA Looks Sport Gel, oils, honey, vinegar.
--My CG and grey hair progress -- http://www.naturallycurly.com/curlta...-progress.html