Oooh, one of my favorite topics. :)
I love cleaning out people's tonsil stones. Did it on my kids. If it were me, and I got them a lot, I would probably go through the pain of the surgery, if insurance covered it.
But you can clean them out yourself. Just use q-tips, the best ones are the long ones you can get at the doctor's office. I think you can order them online, or ask a dr. if s/he can give you a bunch. My dr. gave me some. They are better because the stem is wood and doesn't bend like a regular q-tip does.
So just pry them out with the q-tip. If there's a little blood, that's okay.
The other thing is that you may also have a slit in your tonsils, called a crypt, which fills up with more liquidy, pussy goo, that smells just as bad. You just push around the slit, kind of the way you would squeeze a zit (sorry for the tmi). And the stuff oozes out. My daughter had a ton of it and I spent months expressing her tonsils, but the last time I did it, very little came out.
It may need to be a weekly routine to keep them clean, but you can do it. The worst thing for people's breath was when they stopped routinely removing everyone's tonsils. I'm old enough that I had mine removed. Yay.
p.s. Many doctors and dentists don't seem to know about this, or if they do, they claim ignorance. Probably because they are so gross they don't want to deal with them. But yes, they are real.