My kids seem to have this issue with sticking things in their noses. It's kind of scary at first, but it's not life-threatening. Here are some common methods used for removing an object stuck in the nose:
Unfortunately, if your child jams something way up into his or her nose or just won't sit still enough, these methods might not work. You may need to go to a doctor, and possibly to an ear, nose and throat specialist. Smaller kids can be physically restrained well enough so the doctor can work, but often bigger kids cannot. At worst, if your child can't remain still enough he may need to be sedated so the doctor can get in there with his or her tools to get whatever it is, out.
Recently, our two year-old stuck a LEGO man's arm into his nose. We tried all the regular methods as best we could (with a squirmy, crying child), with no luck. I decided to try something new and perhaps save a lot of trauma, time, and money. I got out the shop vacuum, and with a quick nozzle modification, we sucked that Lego man's arm out of my kid's nose lickety-split!
Now, be sure to read ALL the steps before you condemn me as a terrible, irresponsible parent.... and if you ever try something like this... blah, blah, blah, use common sense, blah, blah, blah.
My shop vacuum was handy, so that's what I used.