Lights dimming as I add lights or plug anything into any outlet
You've lost a wire in your feeder - probably a neutral

And this should be treated like an emergency.  If it was your whole house, we'd be telling you to call the power company ASAP.  

If it's a lost neutral, the problem is that while half your circuits' voltages are going down, the other half are going up - and lighting a 120V appliance up at 190V is a good way to start a fire.   Also, if your main-subpanel connection is the obsolete 3-wire type, a lost neutral is energizing all your grounds and putting lethal voltage on precisely the things that are presumed to be safe.

Fortunately there are only a few places where this problem could happen; the neutral bar in either panel, or the places the hot wires terminate in either panel.  There's also a possibility of wire/cable damage, but that generally happens right after construction of some kind. 

If you have a 3-wire connection (hot-hot-neutral-NO GROUND) this is a very dangerous situation, because as goes the neutral, so goes the ground.