After I pull out my plantar wart will I be able to walk normally again?

Don't pick! Doctors are allowed to pick at things, but that's because we went to school to learn how. We're professional pickers. See a podiatrist for options for treating your wart that don't involve self-surgery!
For a while. You may have some relief of your symptoms after you remove part of your wart. The problem is that it is difficult to self treat or completely remove the wart tissue. Off load the lesion with a pad with aperture and you can get some pressure relief.