Being Able To Feel The Emotions Of People Close To

I am 13 years old and just recently realized something I hadn't before, I like to help people who are going through a rough time, and I can feel there emotion whether it's sadness or confusion. I told my older sister this and she said her and my mother noticed that when I was younger, my body language changed when an emotional part of a movie happened, I know it sounds stupid, even if they were acting, but I was able to feel the real emotion. Anyway I have 2 stories that surprised me because it helped me realize a question. Do I have empathy?

Just recently I was playing Call of Duty (Like any typical 13 year old boy) with my best friend, and we were joking around, messing with each other, and I said something that made him particularly mad, I apologized and we continued playing for the night. I hadn't talked to him for a few days so went on the xbox saw he was playing so I joined his game, but then out of nowhere I felt, sad, angry, scared, confused. Just mixed emotions and they weren't mine. Then we just talked and I apologized again for the other night, and asked him if anything was wrong. He then told me everything he's been through, that he had loved a girl and didn't care about anyone but her. They were just friends, but it took him forever to tell her, and the day he was going to tell her he liked her. Some other guy already did and she had liked the other guy back. He said he was mad at himself for not being fast enough to tell her, he thought maybe things could have been different. But he had excepted what happened and was happy for her, and all he cared about was that she was happy. It's been 4 years since he last saw her, because he moved away. But in those 4 years he's been looking for her trying find her. I felt the emotion of sadness, emptiness he had, I asked him if that how he felt and he said "That's exactly how I feel! How did you know?" I just told him "I don't know".

The next story has to do with my Girl Friend. This was just last night. We were texting and I was just laying down and she said she was playing call of duty. I was going to go online to play a few games with her but then I as I got up I almost fell back in bad because I felt a sadness, loneliness, depressing, feeling like something was going to happen. I asked her if anything was wrong, she said no, so I asked again but more serious, and she finally said "yea I don't feel good" then I felt the feeling stronger, I asked what's wrong and she told me she wasn't getting a reply from her mom (I can't say much because its too private but she hasn't seen her mom in over three years and only saw her a few times a year when she was younger), I asked her not to hurt herself because I felt something was going to happen (She has had a harsh life that no one will really understand unless they talked to her, so she has self harmed befor, and I had stopped it for a while), I told her not to do anything but I was too late she had cut herself slightly, at that moment I knew she did because I swear, I felt all the pain she was going through (there was more going on than just her mother not replying), and I almost collapsed. I was about to burst into tears but I had to call her so she would hear my voice, so I can comfort herself and I told her "Everything will be alright, Just don't hurt yourself anymore please babe. I can feel all the pain your going through, just relax, and I will be there tomorrow and hold you while you tell me everything that happened." We got off the phone and a few minutes later all the emotion was gone other than a calm, Pure feeling and I was about to fall sleep, so I prayed that this feeling last for the rest of the night.

I know the story is cheesy and sounds like a love story but it's what brought my question. I have many smaller stories than these 2, but these ones were the ones with the stronger emotion. Just from these two stories can anyone please tell me if I have empathy?!