Can this institution get away with letting me go after withdrawing the notice?

After being verbally harassed by my teller supervisor and telling a manager who did nothing I put a two week notice in. Then after talking to our hr she told me not to do this to write a letter and it would be taking care of. At the end of my letter I stated "I would like to continue working with this company If we can somehow resolve these issues." At the end of that day I was let go. Technically being fired because I withdrew my notice as my hr told me to do! I have many previous co workers who would speak on my behalf of this behavior that has been allowed! This situation has been very stressful ! I am 23 years old and I worked very hard to accomplish the things I had going for me at this institution. For them to do nothing about the situation causing me to lose something i worked so hard for and loved to do does not seem right!