Depends on lease terms but usually the terms are such that you can't just leave and not be responsible for the remainder of your term. Please check exactly what your lease says about leaving early. The property management likely just meant that they are ok with you leaving (which they don't have to be), as long as they continue to get paid.
It would all be ok once a new roommate is found to take your place and pick up the money that you are no longer paying.
Your old roommate is not obligated to help you find someone to replace you and in fact may be somewhat reluctant to do so given that now they have the whole place for half the price. I know she said she has someone but if that someone did not work out, it is still on you.
What I would do if I were you is pay for March and be real cooperative with them. I would further offer your roommate a $300 finders free if she gets another person by April 1st and $150 if she gets one by may 1st. Plug in whatever numbers above you feel would motivate your roommate to find another tenant for your old room. Otherwise you'd be on the hook for the rest of the term. Also make sure that the property management transfers the lease to the new roommate. Otherwise if they leave early, it may still end up coming back to you.
I hope this helps!

