Am I wrong for this, for cheating when I told her countless times I needed sex and she doesn't care?

So we haven't had sex for months. She complains that she tired from work yet she has energy to go to concerts. I would even wait until both our days off and she crys and complains. So I got tired of asking and told her , I'm going to fuck someone else because I'm sick of her complaining. But nows she mad. Does she have a right to be mad?
Am I wrong for this, for cheating when I told her countless times I needed sex and she doesn't care?
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