1998 Dodge Neon 98 Neon - Pressure and Overheating

I have a 98 Neon DOHC 2.0L engine that overheats after about 20 to 30 minutes of perfect driving. I have replaced the water pump and radiator with new, not rebuilt, parts. I have removed the thermostat all together and bought a new radiator cap with pressure release.

What is happening is the cooling system is building up a lot of pressure and forcing water out of the reservoir. The car then overheats and I have to stop and flip the pressure release on the radiator cap because there is so much back pressure. Once the water blows out of the cap release, I refill the cooling system with water and it will again run cool until the pressure gets so great and the heat gauge is all the way up and I start all over again.

I carry 2 full bottles of water if I am going to drive any distance and as long as I relieve the pressure and put in fresh water it will run perfect. But the built up pressure is so great that it blew up my previous radiator, which is what forced me to buy the new one.

I don''t have any water in the oil or any smoke coming out of the exhaust. The car runs like a dream until it starts to overheat.

Any help or suggestions with what you think might be the problem will be appreciated.