This is looking like swan neck deformity .
Which is mainly seen in Rheumatoid arthritis.
For medications first diagnosis is mandatory so u should do some Blood investigations like ,
CBC ESR
CRPLFT RFT
Serum RA factor
Anti CCP antibody test
Serum
URIC ACID level
X ray hand AP and Oblique
And if Rheumatoid arthritis will be diagnosed then take medicines under doctor guidance with regular followup.
Yes of course it can be treated with medications and physiotherapy and splint .
If it is Rheumatoid arthritis surgery is not required at this stage .
Next Steps
before medications first do investigations for diagnosis