Chest pain can definitely be just a panic attack, I know because I get it all the time. Although I also know that I have high blood pressure, so I take some extra precautions. Is the chest pain constant, does it improve when you walk? Ultimately for me what it took was visiting a cardiologist and getting a stress test to reassure me, not saying you should do this but a trip to the cardiologist couldn't hurt, although I really doubt "with your history of anxiety" that this is anything more than a panic attack.
So yes, panic attacks can come out of nowhere and can DEFINITELY cause chest pain. Im more cases than not we associate the pain with a heart ailment, when what it really is the actual warning sign of an incoming panic attack. Heart attack pain isn't usually throbbing, or can't be pinpointed to a specific area. It is an intense CRUSHING pain as if an elephant was standing on your chest, your entire chest would likely hurt and this pain would more times than not indeed radiate to your left arm although the pain is almost always unbearable to the point where you KNOW something is wrong. Sure some people have "silent" heart attacks, but these are pretty unlikely.
Let me put it to you this way, no amount of reassurance from people on this forum is going to make you feel any better. I know this because the manifestations of my anxiety were identical to yours and I had to go to the ER several times with shortness of breath and chest pain before I accepted that what I had was "Panic Disorder". So what I recommend is a visit to your cardiologist or family doctor to discuss these symptoms, although if I had to guess "not knowing your age or risk factors" I think you can rest easy, but heck a trip to the old heart doctor cant hurt. DVT is extremely rare, more than likely you have pulled a muscle in your lower back or buttocks, and this is radiating into your leg, I know because ive dealt with this myself. Try pushing on the underside of your calf area with your fingers, as well as the muscly area directly underneath your buttocks. Im willing to bet if you press hard enough you will FEEL tension and knots in these areas, if you do you can write off DVT immediately since the pain is INTERNAL and not external IE- affecting the muscles. Also the pain of DVT and PAD gets WORSE as you walk, to the point where you wouldn't even be able to walk anymore without wincing in pain. Not to mention you wouldn't be with us right now if you had DVT that travelled to your lungs, so if you're reading this message you can just about write off PAD or DVT xD.
I don't mean to scare you so don't be concerned, I had a great uncle who died of DVT with a blood clot that travelled to his lungs. He got back from a business trip from San Francisco feeling fine, after the flight he has INTENSE leg pain as well as swelling in his leg and toes. He said he didn't think it was anything, about an hour later he passed away not even having known anything was wrong. My point is DVT is very very rare, and if you had it you wouldn't have enough time to "worry" anyway. Try to get up and walk around whenever you can, not spending 2 hours at a time in front of the PC. I'd like to mention he was in his early 80's, extremely overweight and smoked cigarettes.
Ultimately all of your fears sound extremely similar to my own when my anxiety was at its worst. For me it took hitting rock bottom, going to the ER and INSISTING that I had something seriously wrong with me until they ran any and every test they could, heck at one point they practically believed me. But after this, after cardiology tests, CT Scans of the Lungs and Legs x2, contrast mris that showed absolutely nothing I really had to finally face facts. That week I made a visit to my psychiatrists office, which I had neglected for some time because I was supposedly "Dying" the week after taking the prescription medications he gave me I immediately KNEW what the real problem was.
So anyway take my 2 cents for what it's worth, the real realization that I got to is that as much as you want that certainty from people here on the forums, they just can't give it to you. And even if they could, would you really believe it anyway? xD Rest easy, I hope this little ramble helps somewhat. I am not a medical professional so as always take my advice with a grain of salt, follow up with your doctor and explain your fears very specifically, see if they are willing to run any diagnostic tests... and then learn to accept the diagnosis, it's probably going to be "You're just fine :D"
PS- My chest pain ended up being muscle stiffness caused by panic attacks, as well as back problems from sitting alot that radiate to the chest wall. When I start a jogging regiment, my chest pains dissapear as soon as I return to a sedentary lifestyle they start to return the longer i sit at the PC.