How to heal red dots around areolas after breast surgery? (photo)

The pattern of the marks appears to be sutures that may have bored their way through the skin. The small ulcers left can have a knot or suture material at the base that gets contaminated by skin bacteria and resists closing until the suture is removed. If you feel a prick on your finger when you touch it (like the feel of a single bristle of a brush) you know that is a suture. If you do feel that suture it helps if you surgeon can remove it. Once removed they heal rather quickly. I recommend avoidance of the silicone based gels or tapes if there is a break in the skin as it traps the colonized bacteria. 
I recommend following up with your surgeon for eval, and let them guide you as to what works best for them in their practice.

Dear brbote,every plastic surgeon has his own postoperative protocol which he recommends to his patients. I would suggest you to discuss this with your plastic surgeon. In most cases, this type of healing issues resolves well with time and leave no major scarring. Daniel Barrett, MD
Certified, American Board of Plastic Surgery
Member, American Society of Plastic Surgery
Member, American Society of Aesthetic Plastic Surgery

Hi there, 
Those appear to be your body reacting to the sutures/stiches - I would check again in a few weeks with your surgeon.  
The sutures I use take 4 months to internally dissolve, so this could certainly take some more time.  
I would continue with the Bio Oil as per your surgeon and hold off anything else until you get further advice at your next appointment.
Best wishes!