Hi there ~
I understand your concerns. Having the small hard lump on your neck with pus oozing is a sure sign of infected cyst
that needs to be removed. I think you should see a surgeon for the same and have it excised. I also believe that you should be taking antibiotics to avoid infection. I hope you also visit with a doctor as soon as you can to obtain the antibiotics to contain the infection from spreading to your bloodstream.
I hope this helps. Take care and have a lovely day!