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You should get an upper GI endoscopy done, if the magnet is in the reach of the endoscope, it should be removed on an urgent basis. According to you, it is a single magnet. A single magnet will rarely cause symptoms, but if you have ingested multiple magnets or magnet along with a metal object, you need to get them removed as soon as possible.
For the single magnet, the size of the magnet will decide the course if it has reached into the stomach or small intestine, if it is less than 2.5 cm in all dimension, it should pass down in stools (there are 85 percent chance that it will pass down). Just check your stools for the next 24 to 72 hours. If it does not pass for more than 72 hours or size is larger than 2.5 cm, or the longest dimension is more than 5 cm, you should reach out an endoscopist to get it removed with a grasping forceps.
Investigations to be done:
1. X-ray abdomen erect to look for the location of the magnet.
2. Upper GI endoscopy, if it is in reach of the endoscope (that is till first or second part of duodenum).