Just anxiety?

Hello, I am a female in my early 20's with some concerns about anxiety. I have a HUGE line of heart disease in my family & often get worried my anxiety is something more then just that. Lately, I have been having trouble sleeping. It seems I will be exhausted and as soon as I try to close my eyes, I have what I would like to call a sensation in my heart. It gets jumpy, feels like its floating, pounds hard & sometimes even feels like its just going to stop beating. I even get discomfort in my left arm, sometimes pain. Chest pain and a burning sensation are also common. I dont know if I may have panic disorder or what? It just really concerns me because at the time it feels very, very real and scary. I also get dizzy spells from time to time and it feels I COULD pass out but never have. My doctor has me on anxiety medication but I do not like to take it and do not want to rely on that. What is your personal opinion? Does it sound like a bad case of anxiety or maybe some or something I should further investigate with my Dr.?