I, too, have plantar fasciitis, and mine is manifest in the arches as well as the heels. Arch supports have done more for me than the heel cups that have helped Gail. I use the ProFoot Plantar Fasciitis inserts, and have just recently discovered Orthaheel shoes and inserts (http://www.Orthaheel.ca in Canada, or orthaheelusa.com). I got a couple pairs of their flip-flops from Lands End, and they are very comfortable.
Considering your recent illness, I agree with others that encourage you to pay attention to nutrition and hydration, as your body will deplete the musculoskeletal system of those if it needs to when battling illness.
Heat, stretching, and massage to loosen and lengthen the arches will help – there’s tons of YouTube videos with stretches.
Do they hurt more on waking in the morning, or after activity? Anti-inflammatory pain relievers, like ibuprofen, can help in the short term.