Quick-Clot branded stuff is a type of clay, it forms a solid plug and must be removed by mechanical means when the wound is properly treated. It also heats up in contact with blood, very painful from what I understand, both application and removal.
Celox branded stuff is made from the chitin contained in the shells of shellfish and processed into chitosan. It forms a solid gel type plug. It produces no heat and removal is done by rinsing with water. It doesn't have to be removed, if any is left the body eventually absorbs it. IIRC, there is also a Hemcon brand which is the same stuff applied to bandages.
Dunno about allergies, if the chitosan is what the allergy is to, sure. But they are used so widely and shellfish allergy is relatively common, so I would think not. Of course, new products come out every day so that info may be out of date.