My nephew is showing signs of hand, foot, and mouth disease. My daughter just came to me with a very swollen under eye, any relation to HFMD?

No, but facial . swelling may be. Infra-orbital cellulitis was caused by Haemophilus Influenzae Type B bacteria before HIB vaccines. If your daughter had 3-4 HIB vaccines, starting at 2 mos., she'd be protected. "Strep" & other bacteria can also infect the infra-orbital space. Trauma or allergy can cause it. If not red & tender, apply cool packs & see her MD tomorrow. If red, hot & tender, seek care tonight. .