It does sound like an ice pick headache, which is associated with migraines (which toddlers can get).
A friend of mine told me that he controlled his migraines with allergy medications. My sister and boyfriend have since stopped their migraines (and ice pick headaches in my boyfriend's case) with decongestant allergy medications like Claritin-D (with pseudoephedrine). The problem is that I doubt those medications are approved for toddlers.
You're doing the right thing in bringing your child in for the MRI, but in the meantime, maybe do some research into allergy remedies for children. I'm certainly not a doctor and only have anecdotal evidence, but having seen the amazing effect that decongestant allergy medicines have on the migraines of my friends and family members, I'm sure there's a link between allergies and migraine headaches like the type your son may be having.
Good luck and don't worry - the absence of other neurological symptoms is a very good sign.