Crank fell off square taper BB. Should I replace bottom bracket
Without seeing any pictures, I think you'll likely want to replace both, but you can figure it out easily enough.

Usually, the bottom bracket will be fine after a crank improperly coming loose. The bottom bracket spindle is typically made out of a hard steel and only the most miserable metal cranks are made from anything other than aluminum, so when the crank gets loose, the aluminum gets wrecked and the steel axle stays ok.

However it sounds like you've caused this to happen several times, so you may have managed to round the axle as well.

If you have had many years of use of this bike so far, I think it would be worth it to just cough up 15-25 bucks for a new square taper BB in addition to a new crank and not have to think about it anymore. Your existing BB might be getting worn out already and so you can kill two birds with one stone. You can read the Park Tool guide to cartridge BB servicing. If the bearings are getting worn with age, then it makes this whole ordeal a no-brainer.

Otherwise, if you put your new cranks on your existing bottom bracket, and you pay very close attention to whether it's getting loose or not, you'd probably be fine in determining if the existing bottom is fine, and if it does get a little bit loose, replace the BB immediately and your new cranks should be fine. Do be careful because if they get so loose they come off, you could possibly damage your new cranks.

Ultimately it boils down to whether to pay 15-25 bucks up front, or gamble the price of your replacement cranks that they won't come loose. Only you can decide that.