Sam confidently placed th oars in their locks and started to pull, but we didn't move. Do I need a comma after but in th above sentence?

No.

Yes, you need a comma after "but" in the sentence to separate two independent clauses. The sentence contains two independent clauses - "Sam confidently placed the oars in their locks and started to pull" and "we didn't move." A comma is typically used before coordinating conjunctions like "but" when they join two independent clauses. By adding a comma after "but," you clearly indicate the separation between the two thoughts.