Big toe very sensitive, painful, swollen and red..broken?

Please have this : Checked. There are a number of possible problems. An infection needs to be ruled out. Recommend seeing your podiatrist.

trauma?: Banged your toe? Could be infection, gout, pseudogout (crystal deposition inflammatory disease), other. See md.

Many possibilities: Could be a fracture, strain, sprain, infection, gout, many different systemic diseases, etc. See a podiatrist for a physical exam and possibly x-ray.