Hot end jamming very quickly I have built a 3D printer out of parts from my tip, a ramps board, arduino mega, and a hot end. However, after doing a test extrusion some plastic was spewed out and then the print jammed un-expectantly and my homemade extruder no longer had the strength to push the filament. 

I took the filament out and what I found was that the filament going into the extruder had formed a cylinder at the end. Then after pushing the filament through by hand to eliminate the possibility of my  weak extruder, I found that the filament was expanding coming out of the filament, and then cooling down unable to go through. I cut the filament, removing the bloated end, pushed it back into the extruder and then again after 30 seconds the same problem occurred. 
After researching, I came to the conclusion that maybe there is a gap allowing filament to go out of the heating area, expand and then cool down, or even my wooden direct to bowden adapter is stopping the filament cooling causing it to clog. However I am not sure.

I am becoming frustrated as I am doing this for a school project, I only have two weeks left to finish and everything seems to be failing. Any help would be much appreciated. 

For reference this is my hotend:  link to amazon
I brought the cheapest one available on amazon, so it has no fan and no way to connect a bowden tube. I have created a basic adapter between the thread and a bowden tube holder, out of wood. It's not good but it does the job.

Here is a picture of my hot end and what the filament looks like after I removed it. There appears to be a spiral shape on some of them.
You are suffering from what is called "heat creep". Molten filament is creeping up the heat break and into the bowden tube, where it is causing a jam. You need to install a proper radiator block that is cooled by a fan, not just a lump of wood as a "cold end". The cold end is not just a connector, its primary purpose is to act as a cooler. A hot end on its own is not enough. You also need a cold end. Here is my extruder disassembled (fan omitted). The radiator block is the red item.