Can babies have social anxiety?

My four month old has always gotten so upset when others hold her. I thought when they were this little they didn't really have any separation anxiety but if it isn't me or her Dad or her aunt, the people she's around every day, she freaks out after a minute or two. Even if its someone like my mom, who's been around her many times, she just gets so upset. Also, sometimes when we're just around too many other people or out and about. I wonder if she just gets overwhelmed? Should i let them hold her more even if she cries? Or is this something they outgrow? I hate to see her so upset and also feel bad my family cant hold and play with her 😔