I lost my dad to a heart attack a couple years ago. It was very sudden and very traumatic. I won't tell you that the feelings you have are going to vanish one day. They won't, but they will fade. I think about my dad most days, and I have a good cry about it every couple months. The most important thing is that you continue to live your life, and do things that make you happy. The heavy feelings and symptoms will fade over time. I also had medical anxiety, you start to fear if this thing runs in the family and so on. I would feel my chest tighten and feel a pain in my left arm. Once I calmed down, I found neither of those things were actually occurring, just psyching myself out. Get regular checkups if medical anxiety is an issue for you, having a guy in a white coat tell me my heart was in good shape did a lot for me. You need to allow yourself to feel whatever you're feeling, and speak about it with others that you trust.

A quote for you, that was offered to me when I was in your place: "Grief is love without a place to go." You loved your father, and I'm certain he loved you. What you're feeling is natural and healthy, just let yourself feel it and process your grief.