Yes Emily.

(To the best of my knowledge)
I believe that the body walls off the infection/toxins to protect itself.
What the body has identified as a "foreign body" or toxins must come out eventually.
The sac bursting under the skin traps the irritants inside of the body and causes MORE inflammation of the infected pore or duct to spread the infection...under the skin...INSIDE of the body.

The body just wants it out, or contained if it can't be excreted.

The bump is containing the pus/blood/fluid/old sweat/infection. It stops it from spreading in the body.
Popping the bump underneath the skin, without breaking the skin, seems to make things worse.
That can spread the germs from the secondary infection/s internally and cause other problems, up to and including sepsis.

Tip:
Gently dislodging the built up dead skin around the bump, over time, with a salicylic acid cleanser or benzoyl peroxide acne wash, or other fruit acid peel (fresh lemon juice, papaya, or other) might help.
Keep the area moisturized with a vitamin E oil or other oil or moisturizer that your body tolerates well can soften the skin layers enough where the encapsulated lump may come to the surface.

The body sheds dead cells every day.
Material is getting trapped in the ducts/pores along with sweat, bacteria and sebum without shedding.

Avoid harsh scrubbing. That just irritates the skin worse.

The very warm baths with a capful of bleach, called "bleach baths" have been helping me.

I believe that people get relief once the plug of material is OUT of the body and the pore unclogged.

Hydrogen Peroxide seems to help me flush the wounds. It penetrates the skin and also bubbles on problem areas that I thought had healed or were on their way to healing.

Aloe vera gel, straight from the plant is my "go to".

Take Care
NP

Disclaimer: Not medical advice.

I had one on my hip that was there for years. It started to finally get sore and red so I started to squeeze it and after messing with it for a bit, it's not there anymore. The only way I have found to ease the pain, ironically, is to squeeze as much as I can. However, a lot of people are not as used to pain as myself or as used to the pain. I have been dealing with these things for almost 30 years. It sucks, but you honestly get used to it after so long.

It also has never come to a head or drained anything at all.