You may be moving your elbows forward during the move (especially if you are using a heavier weight). This will involve the anterior delts more. If you keep your bicep curls very strict, and keep your elbows glued to your sides during the move, you should feel less in your shoulders. You may still feel in there some, but you shouldn't feel it more in your shoulders than in your biceps.
Neither way is 'wrong,' it's just that the stricter version isolates the biceps more (which actually isn't very functional, because usually when you do an arm-curl movement in real life, you don't keep your elbows in one place).