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This looks most like Fingertip Eczema to me. There might be a subungual wart in the little finger but this might also just be dead skin build up. I would approach a case like this twice daily application of a super potent steroid like Clobetasol or Halobetasol under occlusion (clingwrap wrapped around the tip and secured with paper tape) for a few weeks. The hands should also be kept well moisturized - Cerave is good for this but needs to be used at least 3-4 times a day, and preferably after each hand wash. Once the eczema is clear any wart tissue will become more apparent - if present this can be frozen off at a later date.
The Psorcon cream used is a mid-potent steroid and often does not work for more severe cases of eczema. Zyclara is for warts and will only worsen eczema. Coal Tar often fails to work in the acute stages of eczema.
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