Cut faces where they intersect with the mesh I exported an object from a game and I am working to clean it up so I can 3d print it. I am almost finished, however I have a small issue with the gun barrel, where I created some new faces to close a gap but ended up with them passing through the barrel tube.

I believe a boolean is necessary but I am very inexperienced with Blender as a whole, leaving me stumped on how to proceed. What can I do to cut these selected faces out of the inner barrel?
In Edit Mode (Use TAB to toggle), Loop select the front inner ring of edges of the barrel by placing your cursor over one of the edges that goes around the circle and hitting Alt+Shift.
Separate this from your mesh by hitting P >> S.
Use TAB to Toggle back into object mode.
RMB over the inner ring to select it.
Hold Shift and select the mesh that you need to cut.
Now go into front view Numpad 1.
Make sure that your toolshelf is open at the left - T to toggle.
Use TAB to toggle back into edit mode.
Select all (Verts / Faces).
On the toolshelf use "Knife Project" - There is a checkbox on the bottom left hand side of the toolshelf that says "Cut Through", make sure you check it.
Now just delete the edges and faces that you don't want.