As a landlord I sometimes purchase sulfuric or muriatic acid to clean clogs out of pipes in my rentals. I have been doing this for years and have never heard of it hardening in the pipes. It always smells awful.
Most likely what happened is that the acid turned the clog into sludge which then clogged your pipes even more. The safest thing for you to do would be to call a plumber and warn him of the acid and have him run a snake through the pipes to clean out the sludge. The next best thing would be to rent a snake yourself and do the job, but I would not recommend this because you seem inexperienced.. However, I was inexperienced once and learned how to handle this by watching a plumber correct my error, and have handled it my self ever since.
I am a landlord and have cleaned out a lot of pipes.