Computer Help and Support

Very often, law enorcement will (with a warrant, please) search browser history.

Also, know that Google (others?) keeps your search history indefinitely (and gives it out, as above) if you are logged into google. Otherwise, they no doubt keep a history of searches from your IP address, and hence "shadow profiles" which hey vehemently deny (they doth protest too much)

Just know that browser history is there. Under a History menu. And that's how you can check to see if a link/site is in your history, and clear it (and cookies and saved data) if you like.

Browsers have become complex beasts. Far beyond the understanding of the average (even above average) users.

Good luck.