Swallowing a little bit of toothpaste is not harmful but swallowing too much toothpaste can lead to poisoning and make you sick.
I have swallowed a bit of toothpaste accidentally before and the only thing that happened is I had a stomach ache for a few hours.
But after a few hours the stomach ache went away and I was fine.
However if you continue swallowing too much toothpaste then you may get intestinal blockage and other possible poisoning from too much fluoride.
If you ingest or swallow more than a little toothpaste or if a kid swallows too much toothpaste then get to a doctor or walk in clinic just to be safe.
Always supervise children 6 years old and under when brushing their teeth so that they do not swallow the toothpaste and make sure they rinse their mouth out and spit the toothpaste out when done brushing their teeth.