Fat Injection to Lips- How to Reduce Swelling?

Lip Swelling following fat transfer
Swelling and bruising to a varying degree is expected. Here are some tips to make it go away faster -
Minimizing Lip Swelling after Lip Augmentation - sounds like you are doing much of the below recommendations
Continued head elevation - sleep in recliner chair for up to the first week
Icing - not directly on skin, 20 min on then 20 min off if comfortable for the first 3 days
Low Salt diet
No heavy lifting, bending over or intense exercise                                                             Bromelain and/or Arnica                                                                                                   Camouflage make up/ lipstick

Extensive swelling of the lips is not uncommon with fat injections.  Other than time and cool compresses there is not much you can do. You may consider oral steroids if the swelling is extreme.  

4 weeks is still early especially considering the fact that you had a rhinoplasty at the same time.  It's likely that you had an incision on the nose that is typically close to the center of the upper lip.  Especially if there was a lot of bruising, it will take longer still to settle.  In the end you should have a nice result.

If it does not settle in 2-3 months, it might be that you have more fat survived in this area than the adjacent areas.  If that is the case, it could be made better either by careful use of steroid injection or micro-liposuction (using the tiny injection tube).  I doubt that that would be necessary.  Wait for the nature to do its thing for now.