Examination:

Finger pulp infection?

(Note: complications of spreading paronychias or puncture wounds of fingers eg gardening injuries, risk of compartment syndrome and subsequent necrosis) 

Management:

Very early cellulitis with soft minimally tender pulp without fluctuance: oral antibiotics (eg flucloxacillin) and early review to ensure improvement

Increased pressure or an abscess in the pulp: the same day referral to a finger surgeon (usually plastics) for usually microscopic decompression of the tiny compartments with wash out of the abscess with antibiotics given while awaiting review