Sounds like the voltage regulator is gone inside the alternator. That's what controls output (more than RPM -- it's not a pulley issue).
You need to get it fixed (or turn on lots of accessories to bring the voltage down) or else you'll soon cook your new battery.
I had this happen to me in my old Honda Accord on a long trip to Muskegon, Michigan and back. I ended up turning on all my lights, blower, defroster, windshield wipers, powering the windows up & down, electric antenna, etc. to keep voltage reasonable until I got home to replace the alt. (OK, maybe not ALL that stuff, but you get the idea.)
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