Is it safe to take st. John's wort and hydroxyzine HCl 10mg tablets daily to help social anxiety?

Yes. There should not be any problems taking both medications except that Hydroxyzine might cause drowsiness. Plus they might not be the treatment for social anxiety. You might need to see a local physician for that problem.
Yes. Saint John's wort can be treacherous as it sensitizes the skin to sunlight. I'm very glad you're addressing your social anxiety. Some folks are prescribed propranolol for this, especially before speaking in public. Ultimately, you're going to overcome this by practice and guidance -- a good, sensible, reality-based counsellor will give you skills and tasks to work on that will help greatly.