This is a well known urban legend.
This letter published on Chest Journal addresses the issue
Trees Don't Grow in the Lungs! \- Chua and Mehta, 2009
> We would like to bring to the attention of readers that trees do not grow in humans. To the best of our knowledge, there has never been a single report in the medical literature of seeds and/or plants growing in humans. If they did, watermelon seeds and peanuts,4,5 which are the most commonly aspirated foreign bodies, would be growing out of control from our lungs. Moreover, it makes no biological sense that in the absence of sunlight and appropriate nutrient medium, photosynthesis and germination of a seed can take place.
>
> 4 \- Mahafza T, Khader Y; Aspirated tracheobronchial foreign bodies: a Jordanian experience, Ear Nose Throat J 2007
>
> 5 Chik KK, Miu TY, Chan CW; Foreign body aspiration in Hong Kong Chinese children, Hong Kong Med J 2009 [PubMed]