After Ultherapy procedure my jawline got really swollen, is it okay to put cold compress or ice in the swollen area?

Ulthera recommends avoiding ice to the treated area when possible because Ultherapy works by triggering inflammation, thereby creating new collagen. However, using ice for a few minutes once or twice will not alter your result, but should be minimized. 

Yes, this should be fine. It can take 6-12 weeks to see results with Ultherapy. I recommend following up with your Doctor for after care. Keep in mind, a combination approach would give the most improvement. I recommend Ultherapy with RF treatments, lasers, microneedling/PRP or sculptra to get increased collagen, tightening and improve skin tone.  I recommend getting a formal evaluation with an expert. Best, Dr. Emer

Icing for several minutes throughout waking hours day of and day after the procedure feels good and wont affect the outcome and tightening should start to become apparent eight weeks post treatment. 

Yes, this will be fine, application of ice and the use of paracetamol will not alter inflammation in the scheme of things. Ice 5 minutes per hour every hour for 1-2 days whilst you are awake. The use of panadol can also help as this is not a NSAID. Keep well, and be patient, results are maximal at 12- 16 weeks. Dr Isobel Walker. Brisbane. Australia.