12,000 gallon pool => PF 12 (120,000 gal = 1,000,000 lbs H2O)

25 / (12 x 0.5 lbs Cl2 per gal 6% bleach) = ~ 4 gallons of PLAIN 6% household bleach. However, if you have a CYA ~ 120 ppm, I'd add 6 gallons. And yes, you can still swim. Just don't wear any new fashion swim suits. People are much, much more chlorine resistant than Lycra!

BUT . . . you are going to continue to have problems without an accurate test kit. I'm guessing your "120ppm" comes from a dealer's electronically read 'guess-strip'? No matter how you read 'guess-strips' they are NOT accurate. Here are your testkit options:
HTH 6-Way Test Kit @ Walmart
Taylor K2006A (3/4 oz bottles) @ Amazon
Taylor K2006C (2 oz bottles) @ Amazon
The Walmart kit is a subset of the Taylor, but with OTO testing (good to have on hand for daily use) and it does have a CYA test. If you can get it now, and order the K2006 (they are NOT available locally!). You'll need to do a 1:1 dilution to test 120 ppm CYA, so buy a gallon of distilled water from Walmart when you get the kit.