Can people see what I Serch from my phone and what I serch with computer and every network I use ?

Your internet activity record is maintained by your Web Browser and you Internet Service Provider. You will need to contact your Internet Service Provider to find out how long do they maintain that data. As far as your browser is concerned, you can delete all saved data at any time.

To answer your question directly, "people' cannot directly see what you are searching for, however, your search history can be retrieved by the right authority if needed.

Axel F.