Will a doctor remove stitches if the incision is infected?

I would definitely recommend visiting your surgeon. Redness is common during healing but can also be an early indicator of complications. Even if some sutures needed to come out I wouldn't worry because 1 week is often when nasal sutures are removed anyway. Good luck! 

If you are concerned you may have an infection, you need to follow up with your surgeon to treat the area. The incision will heal with a better result without an infection, therefore it is essential you follow up for treatment of the area. I would not be worried about the sutures being removed, as this is not always the case and if you leave the area untreated and there is an infection, you may risk more complications. 

Redness may be a sign of infection or a post-surgical inflammatory response.  I think your best next step is to contact your surgeon and discuss your concerns with him/ her.  If you do indeed have an infection, this needs to be treated.  If not, hopefully you will receive reassurance.  Good luck in your recovery!