Hi,
Braces or orthodontic treatment would be your best option to get the teeth inside. Since you mention that you don’t have space, yes you will need to have extraction - because the size of your teeth is bigger than your jaw bone. To accommodate pulling the teeth inside we will have to reduce the teeth matter - hence removing 2 teeth.
Costing for metal braces starts at around 25k and you can even choose to have transparent options.
As for time - usually a good estimate is 1 year but you will get a proper timeline after a consultation.
Next Steps
Next - you can contact us for an orthodontic consultation and discuss the treatment.