you should have your elbows slightly bent forwards, 30-45 degress is usually heaps, just so it takes the pressure off your elbow joints. your arms should all be on the same plane from your shoulders to your hand
Your inner elbows should be facing forwards, wrist should be flat, ie db should be horizontal to the ground.
Sounds like you are trying to lift your wrists,, or the weight is too heavy, your should be raising your arm at the shoulder there should be NO rotation of the arm at the shoulder joint, or wrist., your bi should always be in front never ontop, and your tris always at the back never under.
Start with a lighter weight, stand in front of the mirror and practice. you should feel it in your shoulder and no were else, after a full set of 10-12 you may feel some tightening in your forearms from hanging on to the db and keeping your wrist strait.
The more you bend your arms the easier it will be on your shoulders/wrists, you will see lads doing huge weights, single arm, while supporting themselves on a bench etc with the other arm. they bend their arm more with the much heavier weight to avoid elbow damage. Maybe try this..
Your should start with the weights by your side, lift them to just above shoulder height and lower them back to your side, slowly and without hitting you legs, do it slow, 1,2 up, 3, 4 down, and with control, gut tight, stand strait.
If that still doesnt burn, then hold it for 2 counts with your arms up , parallel to the floor.. dont bend , twist, throw the weights up, swing them in front of you, do the movement too fast, or arch your back.