I had the same problem, lol. I do kettlebells with 15lb. weights and that's made a huge difference. I still don't have the biceps I want but at least the jiggle is gone. Hope this helps. Good luck.
Overhead presses, lat pulldowns, pushups (on an angle if necessary), seated rows and regular rows. Those exercises all work big muscle groups, including the ones in your arms, shoulders and back. Use heavy weights to properly engage all the muscles (heavy for you!).
You CANNOT spot-reduce. Doing crunches doesn't make your stomach flatter. Doing tricep dips does not make your arms less jiggly.
The only way to reduce the fat on your body is to lose weight through diet, and to some extent, exercise. Your body decides where that fat is lost first- stomach, thighs, butt, arms, etc... it's (unfortunately) not something we have control over.
Lifting and strength training WILL tone the muscle under your arms, though. This may give your arms a stronger, more toned look.