Can my parent see my search history?

Yes — if the phone is signed into a Google or Apple account your parent controls, or if parental controls are installed, they can see your browsing history, and it takes seconds, not technical skill. What they cannot see is history from a device entirely on your own account with no supervision software.

Three places to check, all in Settings:

1. iPhone: Settings → Screen Time. If it is on and you never enabled it, sites visited are listed there behind a passcode you do not know. Also check General → VPN & Device Management for a management profile.
2. Android: look for the Family Link app, a parent's Google account under Settings → Accounts, or device-admin apps.
3. Chrome and Safari: check which Google account Chrome syncs to — if it is theirs, your history appears in their My Activity automatically. Safari history syncs through iCloud when a family account shares it.

What does not help: incognito and wiping history. Private browsing still appears in router DNS logs, and clearing history turns a normal conversation into a trust problem. The durable answer is a phone on your own account with your own password, agreed out loud.

For parents: Ultimate Phone Spy is our dashboard for Android 4.0+, Windows and Mac — web history and app activity for a device you administer (web history). It does not support iPhone and is installed openly. Monitoring a minor's phone you own is lawful; the same software on another adult's phone without consent is not.

We covered the longer version in this thread.