After Ultherapy, Heavy Sagging Under my Chin?

This is most certainly post treatment swelling.  This will resolve over time and sleeping with your head and back elevated will also be helpful . The final outcome will take several months.

Ultherapy tightens and lifts facial skin but there can be swelling microscopically in the face that with gravity deposits in the lower facial and neck areas the next day to few days. Puffiness in the skin underneath the chin and neck may be this fluid retention that is expected to go away. One may develop a wonderful result from Ultherapy despite this intiial swelling. 

Please follow up with your doctor.

The information provided in Dr. Shelton's answer is for educational purposes only and is not intended to constitute medical advice.  The information provided should not be relied upon as a substitute for consultations with a qualified health professional who may be familiar with your individual medical needs.

This can be caused from the initial swelling. After the swelling goes down the skin takes more time to bounce back. It should go back after 2-3 weeks and get get better.

If the swelling is new and was not there before the procedure, then it indicates that it is swelling related to inflammation and localized lymphedema. It will go away. Bioflavonods like Swell-X will reduce the swelling as well as sleeping with 2 pillows for a week or two. Read the Ultherapy ebook provided on the link below.