Should I fix my chlorine before worrying about high phosphates in my pool?

Yes. High phosphates feed algae, but if your chlorine level is high enough and pH is in range, algae won’t grow. Check your free chlorine and make sure it holds overnight before buying a phosphate remover. If your chlorine is solid and you still get algae, then lower phosphates with a lanthanum-based remover and clean your filter afterward.