Definitely could be rotator cuff, especially if you tried to control the dumbells as you dropped them or if something pinched in the joint capsule as you rotated the shoulders to drop the weights.
Also, I doubt this would be as much of an issue in the shoulders as in say the elbows or knees (more direct bone-bone impact in those joints), but hydration is a must. The body has to have adequate fluid, otherwise it'll use what it does have to maintain blood plasma volume and other things that are vital -- i.e. it won't produce the amount of synovial fluid, etc. in the joints that is necessary if you're lifting heavy. Also, try some glucosamine or chondroitin sulfate to stimulate fluid production in the joints; that'd help alleviate some of the pain if it's a consistent deal.
As for hydration, I get a minimum of 1.5 gallons of water every day, and somebody your size should probably shoot for 3/4gal-1gal every day.
Definitely start doing some rotator cuff work if this continues to be a problem......you can find a good rehab/prehab program online, I'm sure.
Also, since it's been a couple days, some ibuprofen or naproxen would be nice; it'd help reduce the swelling (if there is any) and alleviate the pain. You want to avoid NSAIDs for the first 24-48 hours to allow the body to go thru the natural inflammation process, but after that they're fair game.
