Allostery means that a protein has more than one binding site for the substrate(s). Yes hemoglobin is an allosteric molecule because it has 4 binding sites for the Oxygen. Hemoglobin can bind 4 oxygen molecules. Yes cooperativity is different, cooperativity, again in Hemoglobin is when one ligand enhances the binding of the other ligand. Of course in order for the molecule to exhibit cooperative binding, it therefore must be allosteric.
I hope the answers your question.