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The lesion in the toe nail is suggestive of onychomycosis or fungal infection of the nail. (with early onycholysis).
Whether to treat this or not is bit controversial. The treatment is an oral anti fungal medication like Terbinafine and the duration can be 6-12 weeks.
No local ointments are usually effective. First step would be to confirm the diagnosis with some testing (usually a KOH mount). You can get in touch with your GP / Doctor for this purpose.
Meanwhile make sure you keep your feet dry as much as possible .
Hope this helps
Please feel free to ask followup questions / clarifications