Can I sue the police and the neighbor?

The neighbor called the police on me claiming she has heard a gunshot coming from my house. The police called my cell phone saying they wanted to have a talk and already outside of my house. So I opened the door for them wondering where they are, next thing I know SWAT came around my house and put me at the back of a police cruiser while searched the whole house. They found 2 pellet guns(1 broken), metal pellets, KNO3, fertilizers, and a home-made smoke bomb. A real gun was never found. Then, the police charged me with mischief, weapon dangerous to the public peace, and possession of explosive material without lawful excuse. I am a third-year university student still attending college and never had problems with the police before nor a social-isolating guy, I just wanted to try something new during the summer. The police prosecutor dropped weapon and explosive charges, but keeping mischief. My big question is whether or not I can sue the neighbor for lying to the police and other related problems caused, such as loss of time(2 weeks in jail), emotional distress, and defamation(I'm a student)? Is it also possible to sue the police for entering on a property without a warrant and malicious prosecution because of the dropped charges?