Is it bad that I blocked my ex girlfriend from social media?

So we broke up on New Year’s Eve because I had an argument with her about her lying to me about going shopping before work because we work in the same place. I had gone in two hours earlier than her. She actually went out with this guy she called her “ friend “ whom I noticed she would text a lot when me and her would hangout. So later that day she was acting distant and I asked her what was wrong and she confessed that she had lied about going shopping before work and told me about going out with that guy. Honestly I had my suspicions about this guy from the moment she added him in Facebook and gave him his number. So when she confessed I got mad and told her “ you really like this guy don’t you?” Then she said I “ I just like talking to him” and I knew she was lying because of how she texted him a lot when We hung out. later I go to her department & tell her That “ if you like this guy so much then why don’t you go with him?” Oh and she also hid his contact from me and kept it as a number. She never added the name so I wouldn’t know who it was but I knew the number already. When I asked her as to why she did it she said “ I forgot to add his name” which I immediately thought was bs. She was clearly hiding it from me. So we brake up and throughout January I was trying to save the relationship. We would hangout and have sex and I noticed that she still texted this dude around me. I kept bugging her if they had something and she would tell me they were just friends, but my gut told me she was lying to my face. So around 3 weeks later she texts me saying that she doesn’t love me like she used to, that we should just be friends. We were friends with benefits throughout the month. I declined and got mad because I did so much for her and her kids throughout our 9 months together. I told her that I would not accept the friend zone and would walk away but the door would be open if she should change her mind.
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So since I was suspicious about this guy I did some investigating. I checked this dudes Facebook and it showed that recently he put on his profile that he got into a relationship. And I’m sure it’s with my ex because I asked her the day after about it face to face and she wouldn’t look me in the face to give me an answer. She laughed because I whispered in her ear good luck with him. I also noticed that she would go to lunch with him a lot. Was a wrong for blocking her if she lied to my face?
Is it bad that I blocked my ex girlfriend from social media?
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