did you have this problem before the new alternator? who converted the truck to an alternator? did you get the same type as was in it before? did you wire it exactly the same as before?
yes, you shoulda listened to yer daddy

the light staying on means you have a dead short somewhere - you need to learn about DC electrical circuits - the alternator does not connect directly to the battery via a fuse .... I'd say your alternator wiring is wrong, grounding the battery back thru the alternator when you turn it off
Bill