Is It Possible to Fix my Teeth Flaring/protrusion Without Extraction of 4 Teeth? (photo)

age:25. Braces on for about 12 months. Initial issues: a somewhat impacted upper canine and flaring. Initially, my ortho said he would try to straighten my teeth without extractions. My teeth are now straight but flare out just as much or more than before the braces. Is my only option to fix this to have 4 bicuspids removed? That is what my ortho is saying now. My mouth is already quite small and my tongue is large so I am concerned. very slight IPR was done on 5 teeth with no benefit I can see.