I know my mom's cheating but I don't have any proof or a way to prove it
Is there a reason why you think your mom is cheating?
Yes, her social media activity makes me think she's cheating with a married man.
It is unfortunate that your mother is doing this to your father. I advise you to tell your father about what is happening so they can handle it between themselves.
I will call my father now.
You are doing the right thing by talking to your father about it. He deserves to know the truth about the situation.