If you are actually towing less than 15K, your current hitch should be fine. If you ever need to tow full GVWR, you could be at risk. Keep in mind full GVWR is considering full propane, full water, black, and gray tanks, and water heater, and the remainder of the weight of stuff in storage bins, cupboards, cabinets, pantry, fridge, and closets. All of that and some dealer added options (slide toppers?)make up the difference from dry weight to GVWR of 3460 pounds in your new trailer.
Keep in mind that 200 gallons of water is about 1800 pounds. So try to keep water to a minimum. A bit more than half of the available CCC.
Might be best to get your trailer weighed while it is full and ready for camping. Then make your decision. If you do decide to get a larger hitch, don't stop at 16K...go up a little higher...maybe 18,000. You may find that Pull-Rite has industry standard rails available for the 18K model. Whether you can use your current bed holes or not? I don't know. But I wouldn't worry about having industry standard rails. Their underbed frame brackets are great. And with universal rails, allow fully clear and open bed when hitch is out.