I've had severe limb spasms that last 2-3 minutes but don't black out, what could cause this?

Many things. You should see your doctor. Potential causes include focal motor seizures (especially if just one limb, or arm & legion same side), dystonia, or simple cramps from things like calcium deficiency. Only a medical evaluation can give you the answer.
Systemic? Localized? A pinched nerve can cause similar. Lack of certain nutrients , like potassium or calcium can cause similar. Do you have numbness or weakness? Would consider seeing a specialist, like a neurologist.