I cannot wear underwired bras usually, although I did find an Avon one a good comfy fit (one of the enhancer/push up ones). I only ever use non-wired ones and find them at British Home Stores or Mothercare. (If in Mothercare look for support bras rather than the feeding ones obviously). Sports bras are good too without the underwiring.
Why, with all the technology available, do manufacturers feel the need to put the tortuous wiring in these intimate garments, they can surely find something more comfortable.
Maybe you have been wearing badly fitting bras? I would go to a good department store like Marks & Spencer or a specialist shop where staff is properly trained to fit bras. Ask them to measure you and help you to find the properly fitting ones. It maybe more expensive than Avon but having a comfortable bra is worth spending a bit more money.
Getting professionally fitted should help (Victoria's Secret doesn't count!) but if you're having numbness and tingling in your arms, there could be other issues in play here.
Many times, nerve and blood flow can be impeded by tight muscles in the whole shoulder area, including the upper back between your shoulder blades, or possibly even muscles in your neck. Wearing too tight bras sure doesn't help, but I'm feeling like that's probably not the cause of it. I suggest anything to help your muscles relax, and once you get a good-fitting bra, work on your posture, keeping your shoulders back.