No, if your parents pay your phone bill, they generally cannot see your search history through the phone bill. The phone bill typically does not record specific details of your internet activity, such as the websites you visit or the search terms you use [1]. However, it's important to note that if you make any purchases that are charged to your phone service, those transactions may be visible on the bill [1].

To get a more accurate understanding of your internet activity, your parents would need to install a monitoring program on your device or use other methods to track your online behavior [2]. It's always a good idea to have open and honest communication with your parents about your online activities and to discuss any concerns they may have.

Learn more:

1. If your parents pay your phone bill, can they see your ... - Quora
2. Can Parents See Internet History On Bill? - Classified Mom
3. Can My Parents See My Internet History on Wi-Fi Bill?