When I first experienced a panic attack, I was fairly certain I was having a heart attack myself.
The truth is, Anxiety mirrors a lot of symptoms that can be related to more serious problems. You're probably not going to feel much better about this situation until you get checked out.
Take some time and go see your doctor. Run the tests and see how it goes. If everything comes back normal, chances are - yes, this is Anxiety. Fortunately, there are many ways to cope with this.
When I saw a psychologist about my Anxiety, he informed me that heart palpitations and shortness of breath are very common with Anxiety and Panic attacks.
I live with Anxiety, and believe me - there are days when the little things that go wrong are enough to push me to tears. It's part of the disorder, in my experience.
I tried medication for a while, but felt that it wasn't for me. Everyone is different. Your doctor may feel that a medication is best for your needs. There are also forms of therapy that can help you deal with Anxiety - even breathing exercises and yoga.
In any case, you're not the first to have experienced this - so, as ironic as this sounds, try not to worry too much! And make sure you stop by and see your doctor - he or she will be better able to help you find out for sure what's been going on.
Good luck.