Right iliac fossa pain for two days with a confirmatory ultrasound is a textbook presentation of acute appendicitis. On colour Doppler the inflamed appendix appears as a blind-ending, non-compressible tubular structure measuring more than $6$ mm, with a hyperaemic wall and possibly surrounding free fluid.
Because the sonographic diagnosis is already secure, the management question reduces to definitive treatment. The treatment of choice for uncomplicated acute appendicitis is operative removal — appendicectomy, preferably laparoscopic.
The alternatives do not fit: a CECT would only add value if the USG were inconclusive or the appendix non-visualised; image-guided drainage applies to a mature appendicular abscess rather than to acute inflammation; and antibiotic-only therapy is not the standard examination answer when the patient can undergo surgery.
Therefore the next step is to operate.
\[\boxed{\text{Surgery — appendicectomy}}\]