To prevent bruising and swelling with Juvéderm lip fillers, should I avoid all omegas? Or just fish oil?

I recommend following up with your injector, but I would discontinue use of these before having fillers.  I prefer to use a cannula to inject fillers to prevent bruising. Look for a cosmetic dermatologist or plastic surgeon who is an expert in fillers to discuss your desired results and concerns. 
I hope this helps.

No, this is unlikely to cause bruising. However, I recommend injections with cannulas to limit bruising and swelling. See an expert. Best, Dr. Emer

Dear haleighgirl,every plastic surgeon has his own preoperative protocol which he recommends to his patients. I would suggest you to discuss this with your plastic surgeon.Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

In my personal experience supplements do very little to create bruising. Majority of patients know if they bruise easier or not. As long as you're not taking aspirin like substances on continuous basis, you should do well. 

Juvederm is a great filler for the lips and to avoid bruising I always recommend discontinuing anything that can cause bruising including the ones that you mentioned.  I give patients a list before injections to prevent as much bruising as possible.  Best, Dr. Green

As a rule, I tell all my patients to avoid any medications or supplements that result in "blood thinning" before having any injection therapies including Botox, fillers etc.  The most likely culprits are aspirin and the nonsteroidal anti-inflammatory drugs.  Theoretically, omega 3 and 6 supplements can cause "blood thinning" and resultant bruising when taken long term.  However, in my experience, that risk is minor and I would not require someone to stop taking this supplement before treatment with fillers. 

In my personal experience supplements do very little to create bruising. Majority of patients know if they bruise easier or not. As long as you're not taking aspirin like substances on continuous basis, you should do well. Good luck from New York City

This is a great question.  I always tell my patients to avoid fish oil supplements but I have not gotten specific about which omega fatty acids to avoid.  I'm going to try to be more specific from now on!
So, omega 3's definately inhibit platelet aggregation and can cause more bruising with filler injections.  Conversely, omega 6's promote clotting (as well as inflammation in general).  For overall health it is better to be on the slower end of the clotting time line but --the slower it is the more bruising you have.  I would stop the supplement for 10 days to 2 weeks before your injections.  
Best of luck to you,
Dr. Amy