Does my 5 month old daughter "know" i am her mother? she seems to be very unsettled with other people even my ?

hubby, her dad, and my mum........one day me and hubby went to a wine/beer/music festival and had to go home early because she was "screaming" and as soon as she saw me she stopped.....and last night my hubby had her after her nap at 5pm and she was crying looking at me with him holding her and as son as she came to me she stopped again.......my mum reckon we need to go to a mum group , i am booking us into mum and baby swimming lessons at our local pool with a friend and her baby too in a few months for summer, but am too shy for a mums group, especially if im the only new one there.....do i need to just do it and book myself in the local mums group every tuesday down the road?? i think so...what else can we do to get her more socially OK?? any suggestions..OH but we go to the shops to do food shoping like 2-3 times a week and she is fine and loves that and also browse around other shops and she is fine........my hubbyreckons its coz she is juts used to me being with me all day.....but eventually we want to have a night out where we can have fun as a couple or with our friends, you know, not all the time but every now and then......and maybe a night to shag eachother brains out like we used too hehe xx