1997 Jeep Cherokee Radiator & Heater Core

My Jeep overheated on the highway and was POURING coolant. After getting it home, we noticed it was pouring out of the radiator. So, I bought a radiator and had a mechanic friend install. I also installed a new thermostat. After driving it home, it began to overheat again, and when I got out of the car and looked underneath I noticed it was leaking coolant again. Since we checked the pressure of the system, I knew it wasnt a leaky hose. But the coolant was leaking out of the overflow well. I have put so much coolant into the system, I wasnt sure if it was the system just bleeding itself out. At any rate, now I notice that the passenger floor is a bit damp. What is strange, is that I drove the car for several miles last nite and had NO PROBLEMS. No leaks. No overheating. Then a few hours later, I drove LITERALLY 1/4 mile and the car started to heat up quite quickly and the coolant was coming out of the overflow again. When I drove it back home, it did heat up quickly, but it doesnt want to overheat, it just stays at about 220. Which is about 5-10 degrees hotter than it normally runs. Is this an obvious heater core issue? Or is the car just bleeding air and the extra coolant? THANKS!