On reflection a number of things occur ot me:

Your boss needs you as much as you need her - I assume you are fairly recently appointed and that she had a hand in recruiting you so it may well be that she has a vested interest in your success (albeit with a funny way of showing it).

Is it possible that she wants you to run the day to day business of the department and she wants to look after the strategic aspects, deal with the bigger bosses and fight her corner on budgets? That could be a good deal for you both and her apparently critical comments may be aimed at helping you deal with running the outfit.

Does she meet you regularly and reasonably frequently and have a honest constructive debate on your role and her expectations of you? Is it customary in your business to do this? I place great store by this.

Just some thoughts - stress at work is very bad, and I hope I may help in some small way.