Which amp do you have? I would first start with the big 3 upgrade, and see if that fixes the problem, because, even if you get a higher output alt, You will need to upgrade those wires anyways.

 

Do the big 3 first, if your still having issues do what I did and swap in a ad244.

How To: High Output AD244 Alternator for ~$80 - S-10 Forum

 

So I finished doing the big 3 upgrade today. One good result was that my headlights seem brighter but the still dim when the LED turn signals blink

 

Something is not wired right on the LED signals than. LED's are supposed to draw less current, not more to dim your lights, You need to get that figured out. I would check the grounds for the signals ect.
Upgrading your alt would not solve the problem.

 

Okay thanks