With redness and swelling of more than one tooth, the most likely explanation is gingivitis (an inflammation of the gum) or other gum disease. It's also possible you have an infection (abscess) around two or more teeth or even a bone infection, but that's less likely. You can read more about these conditions at the links listed on the Sidebar.
Just one last question:
Do you take a medication for osteoporosis or other bone disease, such as alendronate (Fosamax), risedronate (Actonel), ibandronate (Boniva), or the intravenous medication zoledronic acid (Zometa or Reclast)?