It's trespass, and possibly burglary, and makes it easy to accuse you of stealing things. Give your neighbor back his keys and don't give him any more of your things. If the DA decides to press charges, get a lawyer to help you.
You have a right to your property but that doesn't mean you can burglarize another person's property to retrieve what is yours. The proper way to get this accomplished would have been to get the neighbor's permission, to call the local sheriff or constable when your neighbor is home to get their assistance, or to file a law suit to have your things returned.
Even if you have a key, that doesn't mean that you have a right to enter into another person's house or apartment. If they have told you expressly that you do not have permission (and/or have put another lock to prevent your entry), then you are going to struggle to prove that you had permission.
You are likely to have a burglary charge filed against you. I would strongly recommend that you stop talking to the police or your neighbor about this matter and contact a local criminal defense attorney as soon as possible.