hello ...... as per the history u gave, seems like u have got an infection, probably an abscess in ur finger. The fluid collection will not come out by the pin hole, however we dont recommend u to try something like that without medical help. The antibiotic u are taking might be of a lower capacity.
Next Steps
so i would recommend u to visit the nearby doctor soon and get it checked. It might require a higher regimen of antibiotic and may be an incision and drainage.
Health Tips
In the mean while u can send a pic through this portal , in case for further clarification.