Is this depression or what?

To me, this sounds like catharsis. You let your feelings out through art, and more specifically in your case, through music. That's perfectly normal. We all use a different way to channel our feelings and emotions. Many people paint, draw, play music, dance, write, etc. You listen to music and that's a good thing.
I don't think that means you're depressed but it does mean you're probably feeling sad and melancholic, which happens to everyone and is not a bad thing. Try to understand what makes you feel sad so you can fix it.

Maybe you do that because you want to cry. Maybe crying gives you a good feeling, because it's a good relieve. You probably feel melancholic. I wouldn't say you have a depression. There are a lot more symptoms for a depression. I think that when you wallow yourself in sadness, you feel more relieved. It's understandable to get these moods. Personally I often listen to sad music for the emotion that's behind it and sometimes because I can relate to the meaning of the song. I also look back at old pictures, but not with the purpose to get sad. I look at old pictures because of memories. What do you feel when you let yourself get sad? Does it feel like a relieve for you? Do you feel better after?

Though your partner can connect with you anytime anywhere with the blessing of video chat, emails, Skype, still it is bound that you will miss the physical presence or the charm of seeing each other frequently. To maintain such long distance relationship, it is necessary to have mutual understanding, trust, commitment, and overall regular communication with your partner. Therefore it says..:“These lonely nights are hard to get through. I will keep you in my eyes by making you a dream.”https://www.trivedimasterwellness.com/tackle-long-distance-relationship-issues/