PLEASE HELP! MY BABY SCREAMS BLOODY MURDER!

Someone please help! I just can't deal with it anymore!! I don't know what to do! My daughter is 6 months old and ever since she was about 6 weeks, she has been such a fussy baby. She screams out in public when she sees people, if someone comes up to her even a relative she screams. When I go to work, her father has to drive around with her for 3+ hours just because if he didn't she would scream bloody murder and won't calm down. Same goes with when her grandma watches her. I still breastfeed and I work 4 days a week and happens every time I leave her side. I currently just got home. I was supposed to go out with my family from North Carolina to dinner and I had to leave because Ava was screaming bloody murder in the restaurant. I tried to calm her down three times but nothing worked. She's fed, changed, and gave her Motrin 30 minutes before going into the restaurant. I can't help but cry! I just want to give up sometimes. I had random people saying "omg she's a miserable baby" and "jeez she's screaming so loud" and it's so embarrassing. She's not a miserable baby when she's home with me!! If she's home with anyone else and not me she is! And when we're out in public she screams bloody murder! I just can't ever do anything not even grocery shop. I just don't know what to do anymore. Any ideas? Any parents going thru this? Please help. I just want to cry myself to sleep.