There is probably a medically approved method of removing a tick, but this isn't it.
The tick buried itself onto the skin over my left shin a week ago. I noticed it a day or so later. It was hanging on tenaciously to the root of one or two hairs. It had gotten fat from, I suppose, blood sucking, but other than that it wasn't a nuisance, so I didn't notice it right away.
You should probably spring into action immediately, and apply something to convince the tick to let go of the skin, because survival is more important than asphyxiation, or whatever it is its tiny little brain is telling it is important. I have heard gasoline, or fingernail polish, or fingernail remover, or dishwasher liquid, from helpful people who love to give secondhand advice, even though they've never, personally, needed to use such a remedy. This is what you should probably use. As a person who has never, personally, used such a remedy, I am happy to pass on such information to you. Blind leading blind.
This is if you are a sensible person who is medically informed and who is afraid of insect bites. If you are neither, you ignore such advice and do what comes naturally: you pick at it.
I am a fine picker at things. I've dug things out of my skin that probably should have required surgery or anesthesia by trained professionals. Won't bore you with the details, but sometimes a fair amount of blood was involved, but I did it to myself and therefore was prepared for the pain. Some of these things have involved pretty deep gouges, and perhaps the surgical field and the instruments were less than sterile. The only redeeming thing about these self-operations was that healing was quite fast.
The tick's body was grabbable, so naturally, it was the first to get yanked out. The tick's head was surprisingly stubborn. It had lodged itself in there quite well.
A few days after the initial removal of the body, the site of the tickhead was ringed with a swollen and reddened ring of flesh. So the site was infected. Bummer. Also, the lymph nodes in the groin and under the arm on the same side of the infection were swollen and somewhat painful, so it was a pretty good infection. I would pick at the tickhead in a desultory fashion, but every time I did it hurt more, due to the sensitive skin and surrounding area, and the swelling continued.
Took a few days, but I finally removed it. No blades, no surgical knife, just fingernails.
Your body is quite efficient at isolating strange biological organisms that are not your body. The tickhead was encased in a thick brown scabby substance. The more I picked at it, and the more the site bled, the thicker this casing got. Today I was sick of the swollen lymph nodes and the thought that this thing was still attached, that I had a final go at it, and after fifteen minutes of picking this way and that, it finally detached.
This is being written a few hours later. The bite site is looking more healthy already. Redness has decreased, the site is scabbing over, and it's much less sensitive to the touch.
I in no way advocate this as a good tick removal system. If you have a compromised immune system, you definitely shouldn't do this - you should seek medical treatment right away.
However, if you have a normal immune system, and you hate doctor visits, this might be the way to go. If you're still reading this, you probably have a body that tolerates pain. Also, you've had similar experiences with minor self-surgery. It won't kill you. All you need is patience and a bit of time. Again, you probably shouldn't do this. It's a bad idea. Caveat emptor. I'm not medically trained. What do I know?