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3.
Drowsy + Groggy = Droggy. This is most definitely a real word.
I felt really droggy when I woke up this morning.
by Nelli918 April 30, 2012
 
1.
A combination of groggy and drowsy. When you're really tired and disoriented. Comes especially after taking night time pain killers.
'Wow, dude, I'm really droggy this morning, I think I took too many night time sinus pills'
by KristinL May 30, 2006
 
2.
A word deriving from the words drowsey and groggy. I have a friend that drops this like its a real word.
Bill: Dude, lets go to this party.

Ted: Dude I cant. I worked all day and am Im feeling kinda droggy.

Bill: Stop bein a bitch.
by Birbir February 08, 2011