You can make yourself Throw Up by gagging yourself with your finger.
Just stick your finger into your mouth and continue pushing the finger into your mouth until you gag and throw up.
It works for me when I need to throw up to feel better.
Gargling with Egg Whites and even Drinking Salt water can make you throw up.
Although be aware that drinking too much salt water could make things worse and become a medical emergency so only use the Salt water as a last solution.
You could also try gagging yourself by coughing or just act like you're gonna throw up and eventually you should be able to throw up.
There's also the mustard solution to throwing up.
To make yourself throw up with Mustard you mix some mustard with water and then drink it.
The mustard and water will be making you throw up soon after so be near a trash can or the toilet when doing this.