The sole of my left foot was punctured/lacerated by a broken table leg during a fall. There is swelling in mid foot and hurts to walk but I can push through with moderate pain. I can push on the metatarsal and don't believe there is a fracture. There was

See a doctor! Falls are notorious for causing MSKL injury and puncture wounds are high risk for infection. I strongly recommend presenting to a doctor for a thorough history and physical (incl. XRAY) to determine the nature of your pain, evaluate the wound, discuss your tetanus vaccine hx, and provide the appropriate course of care. Home remedies help in some cases, but you need a doctors expert evaluation.
Infection? The main concern here is infection as foot punctures are usually contaminated. The other concern would be a retained foreign body, "sliver" which would increase risk of infection. Get it checked.
Your question was . Cut off. You need to see a doc. If you had a puncture or laceration you need to ensure your tetanus hx is up to date. Xrays should be done to rule out any foreign body, as well as see if any gross fractures. .