flighty_sloth
I think incognito mode unfortunately won't help very much in the scenario you described - regardless which browser you use.
Incognito mode normally allows you to use the browser without a record of your search history, cookies or other temporary data saved on your device. This makes your internet session invisible to other users who share your device. But it is not very effective (or meant to be) in stopping tracking activities, device fingerprinting or even hide your IP address from your ISP and websites - they are all still capable of identifying you.