Okay, I used to pierce ears for a living back in medievil times.
The guns giving allergies is completely false. The earrings are stored in a separate casing from the gun. The gun never actually touches the ear. The worst possible thing you can do is pierce your ears the first time with a needle.
If you've had your ears pierced before, you can repierce them without a gun quite easily. When the holes "close up", it is not entirely closed. Only the top layer of skin on the front and back of the ear has closed. What you need to do (I did this with my teenager) is find, either your original earrings with the really sharp tips and extra long posts, or get a needle and a pair of earrings you don't mind wearing for approximately one week. You will also need to find somebody to do this for you who has a steady hand and some patience.
I highly recommend icing the ear (not only does it help with the pain, but it keeps swelling to a minimum) and having neosporin or some other antibiotic ointment on hand. I swabbed the post of the earring I was going to use with the ointment. I also gave my daughter a couple of ibuprofen about an hour before hand.
If the original hole in your ear went straight through and not at an angle, this should be relatively easy. Sometimes the skin (especially in the back of the ear) can be a little tough to poke through unless you have a sharp needle. Once you get the sharp through the front hole and can see it poking at the back hole put a small piece of potato behind the ear for stability and push hard. Voila, you have just repierced your own ears at no cost to you.