I would be pleased to answer your question .
Yes , it is mostly an infected crust and scab which is oozing out . You should clean it with Betadine
lotion and then apply an antibiotic cream over the area .
You should visit a Dermatologist
who would assess the depth and intensity of infection and might ask for the removal of the nail after the infection resolves.
You might need a course of an oral antibiotic.
Thanks and Take care