Hi and sorry you have this problem. I think it is best to actually get it checked by your GP because you have had it for a month. It sounds like an infection. Do you have a fever? Is it red also? You can try washing it then rubbing some topical hydrogen peroxide on it then let it fizz and the pour some on. Let it dry and cover with a band aide. If it doesn't look much better in a day I would get into the doctor.
mkh9
Well something is under there, whether it is a cyst or an abscess a doctor would be able to tell you. The white stuff you squeezed out is likely pus, which is bacteria and means it is somewhat infected.
For homemade remedy try soaking the bump in water as hot as you can stand with some detol added to it. Dettol is a strong antiseptic aka bacteria killer.