Can peripheral neuropathy become severe and debilitating in a 31 year old woman?

Yes, but. It can, but in one so young, a cause should be identifiable and likely a treatment available. Start with a neurologist.
Peripheral. Yes, peripheral neuropathies can be severe even in younger people. Some of the most common neuropathies are carpal tunnel (in the wrist) and ulnar neuropathy (funny bone) at the elbow. Conservative treatment (pads and splints) can be helpful. Peripheral neuropathy can be worsened by diabetes and pregnancy. Discuss with your doctor and if they can't help ask for a referral to a neurologist.