yea i replaced my alternator with a high output one.. and do have my battery light on all the time.. i did manage to fix it by bypassing a relay in the engine fuse box... wouldnt recommend it as a permanent fix though.. its just making due for the time being

sounds to me like your alternator is dead though, not too hard to replace yourself if you get a new one (or used) just make sure you have a helper.. while you are in there it doesnt hurt to run a large gauge wire from the alternator post to the positive terminal on the battery.. that solved my dimming issues (high output alternator only puts out 80amps at idle.. 150 when rpms are over 850)