What can I do for the swelling and bruising after having fillers to the face?

I would recommend using ice packs on and off for the first few days to help with bruising and swelling after fillers to the face.  Some doctors feel that Arnica can help as well.  I would speak with the physician who treated you to see if they have any other specific recommendations.  

Unfortunately bruising and/or swelling are always a possibility with fillers. Certain areas of the face such as the tear troughs and lips and even Marionette lines bruise more than other areas. If you're on blood thinners such as aspirin or advil, or drink alcohol, green tea, etc, you're more prone to bruising. Ideally no big workout after a filler injection for at least 24hrs, and better yet 48hrs. Your dermatologist can laser the bruise to make it go away faster. For both swelling and bruising, consider an ice pack on & off in the first 24hrs, and you can even try an antihistamine to reduce swelling. Sleeping on your back, especially with an extra pillow if possible, helps reduce swelling. Also, avoid jacuzzi, sauna and steam rooms in the first 48hrs.