The only way to really know if your phone is spying on you is to open the applications and check for any suspicious applications that you never installed.
Check for any apps that may be running in the background that could be spy apps.
Then you can delete those apps and then they would not be able to spy on you.
Yes someone can put spyware on your phone without touching it.
However to be able to remotely install the spyware on the phone you would have to have an account with the cellphone company to install the software.
So for example if you're a parent and your child has a cellphone under your account then you can go online and remotely install cellphone spyware software.
Then you can track down the phone and the child's whereabouts.
Also it can be possible for a hacker to install spyware remotely but they would have to be a really good hacker and it's very unlikely that someone would be spying on your cellphone without you knowing about it.
In case you cannot get hands on your child's phone or do not know their phone's password, you can remotely install a cell phone spy app on their phone and begin tracking their cell phone activity.
This can be done without having physical access to the cellphone.