Some people just have different dispositions and are more prone to throwing up or feeling queasy when training in the heat. Make sure you are well hydrated and as suggested, getting something more than water such as Gatorade is a good idea. Make sure it sits in your stomach fine, many people (myself included) prefer watering down the Gatorade as it is very sweet.
Also make sure you eat a decent meal a few hours before intense training and also make sure that food sits well in your stomach. That is individual so just think about how you feel after you eat a certain food. If you don’t feel great after eating it, make sure you don’t eat that before training.
It sucks throwing up or whatever, but if you are on a team you kinda just gotta suck it up and keep working. Make sure you are staying hydrated and replacing fluids and not overheating. If you STOP sweating that is a danger sign.
Also feeling cold when you should be hot is a sign of heat sickness and at that point you need to tell your coach and stop. He will probably understand. Other than that, just keep pushing. Throwing up sucks but it isn’t the end of the world, it was not unusual for a guy or three to throw up during some of our summer football workouts but you really need to be diligent about staying hydrated and getting a lot of food and drink in afterwards to replace all that you lost.