Detect if Spy app has been put on my phone

That person has to have access to your iPhone. Then the person will need to JailBreak it and then install the questionable apps and all of that without you knowing anything about it while you use your iPhone. Possible? Yes. Probable? No.

Look through your iPhone. Do you see any app and/or folder named Cydia? If you see it then your iPhone is probably Jailbroken.

Have you ever shared your Apple ID and Password with anyone else? If YES then change your Apple ID's password.

Axel F.

Apple monitors and controls the types of Apps that exist in the App Store. Your privacy is important to Apple. There are no spy apps available in the App Store and therefore could not be installed don your iPhone.

There is one exception to the above. If the user JailBreaks his/her iPhone and therefore compromises the security of the device then installing unauthorized apps is possible. If you have not JailBroken your iPhone or no one else JailBroke your iPhone then you have noting to worry about.

Axel F.