I didn't feel nauseous in the morning on invega alone. Make sure you're drinking lots of water.
In America, they do take you to court if you refuse the injection. This is done because the doctors want to relieve themselves of liability. So, if the doctor lets you refuse medication (which is your legal right, by the way), and then as a result you get sicker and do something drastic due to withdrawal/illness, the doctor might get blamed and get sued. To avoid this, they take you to court, so that the court can decide whether or not you need the medication. Now, because of big pharma's corrupt hold over this country's hospitals, when they take you to court, the staff will try hard to make sure to tell only their side of the story and claim you're in need of medication and are going to harm yourself/others, your task is to refute that charge, which is difficult without an expensive lawyer.
The police shouldn't be making any medical claims about your illness, and never have in my experience to me, but if they're saying something about your illness I suggest you get their badge numbers. Doctors don't outright "lie" (in the same sense that police do) so much as they misrepresent. Give them a written notice claiming you're not suicidal or at risk of harming yourself. If possible, have a third party present with you during your visits as witnesses.
If you took the injection voluntarily and avoided court, it's not necessarily a bad thing, since mental health courts are heinously one sided in America (in perspective, mental illness is blamed for mass shootings in this country which are perpetrated by people with a clear written agenda stating otherwise).
The route commonly taken which lets you dodge court fees is to just take the injection and pretend to cooperate, don't give them any reason to suspect you'll stop taking your medication once you get out. However, once you get out, stop taking the injection and move out of state (or if possible, out of the country) for a few months, up to a year.