You need to trust your doctor for his opinion. The decision for root canal treatment is made after a clinical examination and evaluation of your symptoms. Will you ever take a medicine for stomach ache when you have headache??? The suggested treatment is based on the present condition of the tooth. Please don't mind but honestly it is not logical to decide the treatment requirement based on its cost, because it might be the only option to save the tooth. Extraction will definitely be cheaper option but that'll not be the recommended treatment modality.
Next Steps
please get the treatment done as soon as possible for a better and faster healing. delaying the treatment can cause the symptoms to aggravate.