Hi Yogurt! I like your name :-)
Don't worry too much about those smelly yuck ball things from your throat. You're right, they do come from the tonsils, but lots of people get them, at least sometimes. I've had them before. The first one was many years ago, while I was taking the SAT I coughed up a big one! They can be food that got stuck and started to rot and stink with bacteria, or something released from the tonsils (lymph). I remember there was some discussion about that topic a while back here on curezone.
Anyway, you are right to be skeptical about removing the tonsils surgically. I don't think it is necessary to remove your tonsils. That should always be a last resort. Removing them only removes the symptom and not the cause. Tonsils help us out and are a line of protection. What you want to do is get rid of your infection, both sinus, and systemic. Right?
You'll need to clean up your diet to create an environment that doesn't encourage infection. This will include eating lots of raw leafy greens (salad). You might want to go off dairy for a while, at least until the sinus infection clears up.
FIRST of all, I recommend that you use Colloidal Silver , both taken orally (holding it in your mouth, gargling it, swallowing it), and directly rinsing your nose/sinuses. That is a natural antibiotic, it is safe and it works really well. To find out more about that, you can go to the Colloidal Silver forum. Try to start this as soon as possible.
You should also try to clean your lymphatic system (directly relating to your tonsils). This might include massage, skin brushing, exercise, and diet. There is now a lymph forum, as well.
To speed up cleaning your system you could try either a 3-day apple fast, the Lemonade Diet /fast, or juice fasting in conjunction with the things mentioned above. (see Fasting Forum) I recommend drinking green tea daily to help clear the sinuses and bolster the immune system.
I know that might sound daunting but if you poke around a few of those forums I suggested you can get a better idea of the details, and which ones might suit you best, and even more ideas!