1. A screaming, crying infant or young child. The poor couple came in with three screaming-meemies hanging off of them. Now, now, Dorothy—don't be a screaming-meemie! You can play with the toy when it's your turn!
2. By extension, someone who is prone to overblown, petulant complaints. You sure like to dish out insults to people, but you turn into a real screaming-meemie the moment anyone says anything against you. I'm not being a screaming-meemie! I just don't like you talking to me that way.
3. An attack of nervous agitation, as caused by fear, stress, anxiety, etc. Used in the plural. We all got a bad case of the screaming-meemies when we walked into the spooky old house. My poor mother had the screaming-meemies all day as she waited for the doctor to call with her results.