"Don't worry, ..."

punctuation commas period semicolon

Solution 1:

Technically, there should be a semi-colon or a colon instead of a comma.

(On the scale of things, outside of a paper for English class, I don't think many would notice or care.)

Solution 2:

A comma is fine here, and neither a semicolon nor a full stop would be out of place as don't worry and it won't hurt much are both independent clauses. It's a matter of style.

As the link mentions, joining two independent clauses with a comma is considered a comma splice, but don't worry is... je ne sais quoi. For this particular sentence, I don't believe comma use makes for a splice.

If you want to use a comma, you could also say

Don't worry, because it won't hurt much.

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