What is going on with these lines on my cheeks under my eyes?

In my experience, malar creases and tear trough problems do not come about overnight. Quite possibly your recent illness accentuated a process that may have been developing slowly. If in another few weeks the creases remain, fillers, particularly Belotero Balance (in my Upper East Side Manhattan office), would make a good and simple treatment approach. Belotero has little or no tendency to engender the unwanted bluish Tyndall Effect when injected superficially into the delicate tissues below the eyes. In my Israel satellite facility where a far greater number of regulatory agency approved fillers and volumizers are available I would opt for Teosyal Redensity II for this purpose.

The lines that are visible down from the eyes to one's cheeks are ligaments that are more visible especially when one loses volume. This could be due to weight loss, and aging. With strategic injections using Dermal Fillers like Voluma and Radiesse can help revolumize and bring back the apples of your cheeks making you look and feel rejuvenated. 

you have the typical signs of aging, which occurs at different times for different people/genetics.  I suggest a formal cosmetic consultation.  it may be best for you to start mild laser/peel treatments, some fillers, and better skin care to help prevent the process from rapidily progressing.  Best, Dr. Emer.

I guess after the stomach flu, you may lose some weight, and those lines became more noticeable, but most probably you had them even before the flu. You can benefit from a filler like Belotero in the U.S. or Juvederm Volbella, that is not approved yet in the U.S. but is approved in Mexico and most of Europe. Volbella and Belotero can be injected more superficially, with less chances of getting a Tyndall effect on the injected area. Volbella in particular can last for up to 12 months, very minimal discomfort with the injections, as it has lidocaine .3% and minimal recovery time.

Facial volume loss do to ageing is a slow, gradual process.  Perhaps dehydration has accentuated these creases or have made you more aware of the creases.  Wait several weeks (6) to see if there is improvement. If there is no improvement a hyaluronic acid filler to the tear trough and cheek creases will improve the appearance.