Yes, solvents have varying degrees of toxicity when inhaled or absorbed through the skin. I've often wet my hands with methanol, or acetonitrile, and not felt the bad effects you describe, and your exposure sounds similar to mine. But I wasn't there with you, so I can't be sure.
It is your and the people in charge of the lab's shared responsibility to read and understand the MSDS for any reagents you use. Look online now, and see how what you remember of the exposure level compares with the LD50 for methanol, and for the description of the effects, also in the MSDS.
Then consider if a trip to the emergency room, for a more through check and treatment if warranted.