Proteus, or Proteus mirabilis, is just a type of bacterial infection. HS has absolutely nothing to do with bacteria. Remember that, because it's very important. And a lot of GPs don't seem to understand that.
The initial cyst is just an inflammatory reponse, and the puss that makes up a HS cyst is just a bunch of white blood cells. However, it is very common for these cysts to become infected, but the primary cause of a cyst caused by HS is not bacterial in nature. That's what separates HS from things like MRSA.
For whatever reason, when mine get infected it's always a proteus infection. I've never had staph or anything else turn up in any of my cultures (sadly there have been quite a few samples taken).
I've done some research and that seems to be a pretty common bacteria in people with HS. There was a medical journal published in Poland I think that listed the most common bacterial infections in HS boils. I think Proteus was #2, don't quote me on that though.
To be clear, not everyone with HS gets infections, only the lucky ones. Yay us. I honestly can't tell you why some people can go through their entire lives with HS and not have a single infection, where others, like moi seem to get infected at the drop of a hat.
It is possible you're progressing into another stage of the disease, or it could just be spreading to another part of your body. I'm not sure what areas are usually affected for you, but over time HS does tend to spread and even though it's usually concentrated in the armpits, underboobs, groin and anal regions, it can spread anywhere you have hair. And you can have different stages in different parts of your body.
The antibiotics have been working as an anti-inflammatory, although from what you've said it doesn't seem to get rid of your lumps entirely just keeps them under control. I'm not sure if you've been taking them long-term or just as needed, but either way, it's certainly possible you've built up a tolerance if you've been taking it for more than 3 months. Your doc might recommend another antibiotic in a different class if this one's been working for you.
As far as whether or not it needs to be lanced...that's sort of in the eye of the beholder, or doctor as it were. Some doctors would rather put you on antibiotics first and lance as a last resort, others just say forget it, let's drain it. Once an abscess reaches a certain point though, usually when it starts causing fevers, chills etc, or just causing you too much pain, a doctor will just go ahead and lance it. I've always gotten an antibiotic after the fact to kill whatever else is in there.
I'd personally recommend getting it lanced, only because relief is pretty much immediate, after you get through the nail-biting experience of being numbed anyway, and they'll be able to send the puss out for culture and give you an antibiotic that will definitely kill whatever bacteria is still running around inside that boil, instead of just best-guessing it. I can't even tell you how many I've had lanced, if I had to guess, probably around 2 or 3 dozen.
Just to give you another option, because nobody likes the idea or the practical application of lancing a boil, talk to your doctor about the possibility of a corticosteroid injection. Again, it's a powerful anti-inflammatory, but it's injected directly into a cyst and usually reduces inflammation significantly within the first 24 hours, and continues to work from there. It's not a long-term solution by any means, especially since they can only give you so much within a 6 month time span, but sometimes if I had a pea-sized lump that morphed into an infected golf-ball overnight, I'd make an emergency appt with my derma and he'd just inject me, give me an antibiotic, and by that time the next day it was mostly gone, and pretty much flat within 72 hours. Never stopped them from coming back, but it was a lot less painful than lancing, and I was able to go in on my lunch break rather than taking the rest of the day off. He only did this after lancing two or three and determined what type of bacteria we were dealing with though.
Now here's the good news , if this is the first cyst that's popped up in that particular area, get a dermatologist to surgically excise it. Do it now, before it starts to develop sinus tracts and spread out, and you might prevent more from showing up in that area.
Definitely go see your doctor, I know it's a pain, but it's just going to get worse if you don't do anything. Let me know how it goes!