1 week after CoolSculpting. Swollen. Can injections lift my face?

Without looking at the before photos and the area of Coolmini applicator placement, it is hard to judge what exactly happened. It is possible to have the swelling in the neck for few weeks and usually subsides on its own. Speak with your physician and have him examine you.
Best of luck
Dr. Shanthala

Hopefully you didn't actually have Coolsculpting of the face as this is not a recommended treatment area. Please clarify this with the office. 

The only place you can put the cool mini is under the jaw line straight under the chin OR in a v pattern slightly overlapping in the middle but reaching side to side. The jowel area is above where any cool sculpting would be so I'm not sure what your provider might be planning but if something doesn't feel right make sure you're seeing a Board certified provider like a plastic surgeon or dermatologist for best outcomes. Best of Luck.

After the CS, there does tend to be some swelling of the area that can last up to several weeks - I have heard this from many of my patients and have experienced this myself when my body was coolsculpted. The swelling almost goes away instantly around the 3rd to 4th week and results become apparent.  On week 4, I often hear folks telling me that they saw an immediate recution and now they can fit into jeans they could prior to their pregnancy,
Hang in there, I would wait a few more weeks before trying anything else, you probably will get great results.
Remember, it take 90 days to realize the full results and usually I see most results in by 60-70 days.  You should be perfect for your wedding and congratulations!

Thank you for your question. Swelling after CoolSculpting is expected and the degree of swelling will vary from one patient to another. It usually subside within 2 weeks after the procedure. It is too early to know if you need another treatment. I am not sure where the applicator was applied, but it should be under the jaw line and chin. I hope this help. All the best, Dr.Michon

CoolSculpting should not be placed on the face for several reasons, but it can be placed on the submental area (below the chin) which generally has good results.  I'm not sure where your applicator was placed but swelling is not unusual, especially after one week.  I would wait to do any injections as it takes ~6-8 weeks to see any results from your first CoolSculpting treatment.  We recommend two sessions of CoolSculpting for optimal results.

Swelling after CoolSculpting is a normal expectation. Was the applicator applied right underneath your chin? I would wait until the swelling goes down before moving forward with any other treatment.