im assuming you have the manual for this radio already, but if not, here is a link:
http://www.cbtricks.com/radios/cobra/29ltd_chr/graphics/cobra_29ltd_chr_om.pdf
just to make sure you are checking the SWR correctly.
i understand that you actually do have some sort of antenna problem because the AWI is coming on.
try unplugging the coax from the antenna mount.
now check the antenna using a multimeter by using the continuity function or the resistance function and touching one lead to the antenna whip and the other lead to the vehicle body.
there should be no connection between the two, otherwise known as an open connection.
now check the coax that you just removed from the antenna mount the same way.
again, there should be no connection. (the other end of the coax should still be screwed into the back of the radio)
if you find shorted connections on either of these tests, you have an antenna mounting problem or your coax is bad. could also be a bad connection on the PL-259 connector that plugs into the radio.
did you use a soldered connector here or one of those non-soldered connectors from radio shack?
remember that large metal objects within a foot or two of that antenna can cause problems.
good luck,
LC