The 105amp is just weak, they struggle to handle the load of the headlights and blower motor. They come with a warranty I have my receipt in the glovebox. I replace mine about every 1.5 battery life cycles, always goes out in winter. If you upgrade to a higher amp just be sure the mounting holes line up.
Check the cable from battery to alternator.
A bigger alternator is not a bad idea, but without upgrading the charging wire, your still trying to recharge the battery through a very small wire. The big 3 upgrade, will help a lot with this. Even better, adding 2 extra ground wires ( 1 to the cab, and 1 to the battery, from the alternator case), also helps. I used a #2 welding lead, but
@5vortec7 sales a very nice kit. Then the other thing is, at idle the engine doesn't turn the alternator fast enough to make the alternator charge at a higher capacity. I also got an overdrive pulley for my alternator. I went from around 9 volts at idle, with a full load, to 13. And all of this on the 105 amp alternator. Just a FYI