When last I worked in law enforcement (2015), all offenses from other states appeared on your driving record, so yes, the information is shared with your home state. Since the "point system" differs from state to state, you would be assessed the number of points your home state would give you for the same offense.
Best advice -- Read both sides of the ticket carefully. Follow the instructions to take the ticket to court. Tell the prosecutor you realize you were over the limit, that your conduct that day was an aberration, that you have an otherwise-good driving record and are a safe driver. Offer your excuse -- IBS, urgent need to reach a restroom, etc. Let him or her know you are here to request leniency to save your license and see what they can do. Ask for their help.
Be prepared to pay a fine, and offer to take a safe driving class that your state / DMV accepts.
You may get that offer to plead guilty to a no-points violation, or a greatly reduced speed with fewer points, or even a "first offense" program by any of several names -- "probation before judgement," etc., where you pay the fine and they put an entry on your driving record that goes away in a year as long as you get no new tickets. Many states have this type of resolution, but I'm not sure about New Jersey, a state notoriously strict about moving violations.
Two things to remember: If you take a "first offense" program and agree that you won't get any more tickets for a year, DON'T. If you do, you'll really be screwed; and 2) Your insurance company is still going to raise your rates.
For the record (after reading some of the comments here
I went to more violent domestics than the number of tickets I wrote
I always reduced the driver's speed down to 9 over;
I did not eat a donut for 25 years, but I did buy coffee at those donut shops... and bagels, usually because they were the only places open in the middle of the night. I often wondered how many cops had coffee and a donut for their last meal.