Is it normal that i constantly worry in a relationship?

So I was in a relationship with a guy for more than a year. Once I realized how much I cared about him, I would have what I would call "anxiety attacks" whenever he went out. I would daydream that he got in a car accident or that someone would shoot or rob him wherever he was or that, if he was playing sports with friends, someone would hurt him. I think it might have something to do with the fact that when the relationship started, he had just torn his ACL and meniscus and had just had surgery, so I was always kind of caring for him. After that surgery, he never wore his knee brace when he was supposed to, and I would literally cry when I found out that he hadn't worn it. I would worry so much that it'd get worse and that he'd be in a wheelchair the rest of his life. Another time, he broke his finger at basketball. I knew that the people he was playing with were rough and I told him not to go, but he did anyways and he broke his finger. I cried then too. Then, whenever he would "forget" his splint or "lose" his tape for his finger, I would get super upset too. I just couldn't handle things that other people, including his parents, seemed to not worry about at all. The relationship is over now and I see how crazy I was acting, so I want to know, is that kind of behavior normal or do I really need to see a therapist of some sort to talk about my anxiety issues? I'm scared of getting in a new relationship now because I fear that behavior will return and make me miserable and drive him away like in this last relationship. Help!