Step 1: Treat this as eponym recall. Tom Smith is the name attached to a specific infective hip condition seen in the very young, so focus on the infancy angle.
Step 2: Build the clinical picture. It is a septic arthritis of the hip in infants, presenting acutely with quick abscess formation that may discharge or be drained and then heals. The damaged joint gives a positive telescope test from gross instability.
Step 3: Because the hip ends up dislocated and unstable, the appearance can mimic a congenital dislocation of the hip, yet the underlying mechanism is infection in early life.
Step 4: Reject the other choices - it is neither gonococcal, nor a smallpox-related joint disease, nor a chronic pyogenic process - leaving septic arthritis of infancy as the match.
\[\boxed{\text{Septic arthritis of infancy}}\]