Welcome to PC! I love this forum - everyone is super supportive!
I just started a MSW program and I have similar fears. I'm also concerned that my clients will be able to pick up on my insecurities as well as my own mental health struggles. I have a friend who has similar issues as me who is working as a social worker and is great at her job. One thing she says that helps her is learning how to compartmentalize - to leave her own issues and insecurities at home. Much easier said than done though.
Also, I think/hope that the feelings of insecurity will lessen when we gain more experience. I think to a certain extent that feeling is common, especially in new grads.