I solved the problem...I realized that it was only giving me double alerts when people were sending me imessages instead of SMS. I had the setting of "allow confirmation of message received" off.
On their end, they had the setting "Send over SMS if imessage fails" option on. I think what was going on was my phone was denying imessage confirmation, and they were re-sending as an SMS. My phone was merging the message (changed from "imessage" indication above the message to "SMS").
After I turned on "allow confirmation of receipt," never had the double message again.