What can happen if a small ant crawls inside the human body through nose or ear?

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The worst thing that can happen to that creature is that it will die. No insect after entering into the nose can survive for a long time as it usually gets pushed into the stomach and gets killed due to gastric juices. Yes, some organisms like worms survive the effect of gastric juices and can survive at the cost of the body. An insect in the nose usually, if alive, can produce severe foreign body sensations, and you would either sneeze it out or, if stuck, seek immediate medical help to get it out. Once an insect goes into the nose or ear, the feeling that it is still there is often psychological, even when the insect would not be there.