fuck this job.com

The security guard at my job is making me feel insecure. When he first started talking to me, he was acting pretty nice (actually, pretty flirtatious). However, a few days later he calls me dumb (some people are so full of themselves!)
I saw him in the mall 2 weeks ago, he tried to to say hi to me, but I walked away. He followed me to my other job and said "we work together! why didn't you say hi to me!?! I was really worried" and I told him I'd talk to him later. After I got off, I went to my other job and I confronted him about calling me names. He tried to pretend like he didn't know what I was talking about, so I walked away. I told my boss and his that he followed me through the mall and annoyed me at my other job, while I was with a customer. Ever since then, whenever I see him I get really angry, my heart rate speeds ups, etc.
Should I try and talk to him and ask him if we can be "civil" and "keep things business", hoping to make things at work more pleasant? thanks for your feedback.