Episiotomy (Surgical vagina cut and sewing)

I'm quite nervous and curious about Episiotomy. As a first time mommy to-be, I heard contractions is not only the pain that we have to go through but some need to go through episiotomy if there's a cut. Now the question is does it hurt alot to feel the cut from the doctor throughout the delivery process? Or we will not feel it? It's not that I don't believe my mum but I thought she probably might just want to calm me down by assuring that it's not painful and we will not feel the pain when the doctor gave us the cut while the delivery process as we will focus more with the pain of delivering and pushing. Is that true???? And also before the doctor even stitch up the cut, do they gave any anesthesia or a cream that makes our skin numb on our vagina??? Really hope any mommies that have gone through this experience could help me to get the answer so I won't be too nervous. Thank you and stay safe! ❤️ #1stimemom #pleasehelp #firstbaby #pregnancy #advicepls