Droid 3 question - Help!!?

Just bought a Droid 3 with service from Verizon and I'm having some issues. I can turn the phone off and it will power back on by itself. I''ve read several sites online that state this can be an indication that "spyware" has been added to the cellphone. I'm going thru a bad break-up & several things that "John" has said leads me to believe he has loaded a tracking program either on my phone or thru his home computer. Can software or spyware be added to a phone without your knowledge or is there a program you can use on your home computer to track someones whereabouts and/or phone activity? I feel like I'm being stalked - help?