If I had a paranoid girlfriend that spyed on me all the time "Trying to catch me do something" she wouldn't be my girlfriend long. Particularly if I wasn't doing anything to begin with. Fidelity might be assumed if you are "engaged" or "going steady" but its not a right until you are married, but certainly not when you are "just dating".
Want to destroy a relationship... thats a quick way to do it.
If you have paranoia and OCD type needs to prove someone ISN'T doing something, then its time for therapy.
If he really is doing something then its time to move on...