What do I do if I'm accused of stealing and I didn't?

Instead of fighting with them or yelling, Find your mum and say ‘hey mum, I need to talk to you… I honestly didn’t steal your jewelry, I know and I understand why you would blame me, but I am telling you the truth, I didn’t do it.’ or something along those lines.

Be reasonable and don’t raise your voice. Your mum is more likely to listen to what you have to say, than your dad.

What I would do, is talk to them one last time, tell them “look me in the eye, I’m your son, and I’m NOT lying to you, if you don’t believe me, your son, your blood, then I don’t know what else you expect me to do…”. Just make sure to look at them straight in the eye. Considering they have no idea where the jewelry went, they shouldn’t be cutting off heads, especially when you’re their son. Is there anyone else in your house that might have taken it (a brother, sister, etc..)? Tell them that you’ll help them look for the lost jewelry & hopefully they’ll understand you’re being genuine and honest.

Talk to them calmly amd tell the that you did not do it, let them know that they can go trough your stuff and go trough what the want, tell them that you are willing to prove tjat you did not do it. If they don’t believe you then leave the subject alone, and tell them that you know you didn’t do it and that your not going to let that bother you.

Since you have a history, your best action is to be honest, answer any questions, deny you did anything and then survive the storm. You need to rebuild your credibility. They aren’t going to believe you until you show you are honest over a period of time. It sucks. But you dug that hole. You will not be believed until you are consistent and honest. Unfortunately, this will take time. Some of your friends or relatives probably believe you. Keep them close and talk to them. Eventually if you are honest, everyone will come around. It will take time.