2001 Cadillac Seville sets over heat

I have a 2001 Cadillac Seville sts. When me
and the wife got it the guy said it would run
hot from time to time. So I ran a block test on
it no results of exhaust gases. Come to find
out it was a fan not kicking on. So fixed that
drove it down the road and the upper radiator
hose busted replaced hose. Then the radiator
busted on the upper hose side. Replaced that.
Now I’ve noticed I have pressure in the lower
hose and no flow in the upper both hoses get
hot and the expansion tank is building
pressure high enough coolant pushes out of
the cap. I have checked the purge line and the
nipple on the water pump housing is clear but
it only spits coolant out here and there I have
pulled the thermostat and bypassed heater
core only thing I haven’t done yet is the water
pump. Can anyone help me with what else
maybe causing this or is this something the
water pump will do if the water pump isn’t
working?