Stitches after giving birth

So I was discussing giving birth with one of my friends last night and I have a question. This may sound ridiculous, but I genuinely don't know the answer.

If you tear during birth and need stitches after, do they just sew you up as you are? I mean, I assume it wouldn't be as bad as the actual birth, and they probably wouldn't want to be jamming needles into your traumatised genitals to give you a local for numbing, but I just wasn't 100% certain.

For some reason, the thought of being stitched up with no medication bothers me more than the thought of the birth 😂 (I'm sure I'll change my mind when I'm giving birth).