2003 civic overheating
 

Hello,

I have a 2003 Civic Ex Coupe with an automatic transmission. A couple months ago the heater core went out, leaking antifreeze into the passenger foot area, but being a student affording a mechanic wasn't an option, so for the time being I cut the hoses going to and from the heater core and coupled them together (I'm not sure if this has any impact on the current issue or not). After doing so I filled up both the radiator and the reservoir.

Current issue
Recently I've noticed that the engine temperature gets pretty warm in slow or stop and go traffic, the longer I'm stopped the higher it got, never getting into the red. However today on my way to work, in terrible stop and go, it made it past the red and began smoking, I pulled over, the smoke (it was probably steam) was coming directly from the radiator cap, there was splashed antifreeze around the cap as if it was boiling out of the cap. However when I went to add water to the reservoir, it was totally full, exactly how it was a few months ago. I waited until the engine was cooler and continued to drive to work, however the engine didn't get cooler as I reached higher speeds like it used to it would just heat up and stay hot. So I pulled over, turned on the car without turning on the engine, cooled it to half way, drove more, and repeated this until I got to work.

Ideas as to what the problem is
Based off of what I've searched it seems some of the possible issues include air in the radiator, bad radiator and/or thermostat, blown head gasket, radiator is out of coolant, or a bad fan, (however I did see that both radiator fans did run while I turned the car on but left the engine off).

Any ideas as to
a) What the problem is
b) How to fix the problem
c) How to get the car home in one piece to fix it without getting a tow

Thanks so much for the help, sorry for the long post