Throwing up when introduced to different textures might be a sign of Sensory Food Aversion/Sensory Processing Disorder (please refer, for example, to this article on NYT, or this one on WebMD).
My now 4-year-old child used to live exclusively on a liquid diet since it was 12 months old. It has been recently diagnosed with SPD and life has started to improve since we started treatment.
If you have tried other tips and tricks for picky eaters and none of them worked, I would suggest you look into this.
Here is a useful blog entry on the issue:
What is a Sensory Food Aversion?
When eating, you are exposed to a significant number of sensory inputs. From visual appearance of food, smell, temperature, taste and texture, eating is a demanding experience from a sensory perspective. Some children are over (or under) responsive to the sensory elements of food and eating. This can mean gagging at the sight or smell of certain foods. It can also be vomiting or spitting food out. Sensory food aversion can occur for many reasons, but often it is the result of difficulty processing the sensory aspects of eating. Children with an aversion are often labeled as picky or selective eaters.