You can use warm/hot damp compress on the area to help it open and drain. This will also stimulate blood circulation to help fight infection. It should draw the infection to a head and may help the BB pop out as the sore opens to drain.
If the sore does open and the BB comes out you can clean the area with betadine iodine solution, chlorhexiderm solution, sterile saline, or 3% hydrogen peroxide.
You can then apply neosporin or triple antibiotic ointment to wound and any scabbed over areas to help fight infection.
Best option would of course be to see the vet to get the BB out and get any needed meds to fight infection but if you cannot do that then hot compresses several times a day may help the cat fight the infection.
Hope this helps you!
Would it be alright to wait a day or two to go to the vets?
If you wait then I'd do the home care to help limit how much the infection might spread.
If the cat is eating and drinking OK and not seeming overly ill then you may be able to wait.
I will. I am just afraid. I had a nine month old kitten that I had to put to sleep two weeks ago because of FIP. Plague is still eating; drinking; and behaving very normal, except he is staying inside more, when is prefers to be outside all of the time. I think he may be staying in due to the cold weather we are experiencing right now.
Plus if he is not feeling well from the infection staying in where its warm will feel better to him than being out in the cold.