hiya i can completely relate. anxiety can cause a whole load of unpleasant symptoms to the point you believe there is something seriously wrong, but there isn't. heart palpitations are awful but common with anxiety. i also experience the lightheaded feeling and normally when i have an anxiety attack i do get the pins and needles in my hands too!
for your breathing you could actually be hyperventilating so when you feel you aren't breathing properly there are loads of apps you can get on your phone where you follow a circle with your breathing so it could be breathe in for 6 seconds hold for 2 and breathe out for 6 seconds (example). or if you haven't got your phone what i do when i feel that way even if i feel like i'm not taking in air is to take one big breath all the way OUT so there's no air in my lungs at all and then it helps me regulate my breathing.
meditation is helpful as well i think. try to learn to accept your symptoms are anxiety and in time it will get easier. good luck