Checking your boyfriend's twitter.. Do you think I have the right to check?

[BeautifulVixen]

Recently I have asked my bf if I could see his twitter password to see how serious we are in our relationship. He got upset about me asking for his password so I assumed that there is something that he was hiding. So in this case I checked his twitter timeline to see what was going on. & I saw that he was flirting with other girls and was trying to meet up with them. We are both still young, im 18 & he's 20. By looking at his twitter timeline I can see that his DM (direct messages) were full of him conversing with these girls. In the past we have had issues with random girls that he flirt with online and meeting up with them. I believe that he is just addicted to socializing and flirting. He doesn't know that I have already seen a glimpse of what he has been about. This is extremely stressful and I am going to finally let him know what I've seen today once he get off work. If he doesn't let me have his password or show me that he's going to stop then today will be my last day being with him, I can not continue with this type of relationship. But before I tell him about looking into his twitter do you think that I have the right to check? or do you think im doing too much?