Can someone tell me how long will it take for my incision to heal after thyroid surgery?

Depends. It depends on how the incision was closed. Traditionally it is closed with a thin suture and steristrips which would take 7-10 days to heal but the bruising could take up to 2-3weeks. .
Thyroid incision. The incision will heal fairly quickly. Within a couple weeks it should be minimally pink/red, nontender and free of any sutures or closure material. It will be susceptible to effects from sun exposure for up to a year. I generally recommend at least 50spf sunscreen on any head and neck incision with exposure for at least 1 year.