There is no need for you to go to the doctor now as you are recovered.
You are very lucky that you did not die. I hope this episode will stay with you so that you remember not to drink so much again.
A young cousin of mine drank too much vodka at a wedding unbeknown by any adult. Luckily for her another relative found her and had to give her mouth to mouth resuscitation and she had to be rushed to hospital whilst throwing up, where they pumped her stomach.
It does not have to be vodka, it can be any type of alcohol, even wine and beer, in fact all alcohol, if drunk excessively will make you ill. Not only that it can damage your liver and other internal organs as well as destroying brain cells. Alcohol is also addictive, so it is best to limit your intake and have a drink occasionally. One average sized glass of wine is fine with a meal.
When you have a drink again, stick to safe limits, you can find the safe alcohol limit to drink on the web. But even the safe limit of alcohol may be too much for you, so listen to your body too. Also do not mix your drinks, this will make you feel very ill too. I feel drunk after one small glass of wine even when I have it with a meal.
And like the previous poster says, eat something first before you consume alcohol and drink plenty of water. Alcohol dehydrates the body. You could have easily died by choking on your own vomit too and you had no one to assist you.
At the age of 19, you are obviously experimenting and having a go at different things. And you have learned first hand for yourself now how it feels to be completely "blottoed". So you can avoid the situation in the future.
"Bottoms up". (an expression when people raise their glasses to drink a celebratory toast).
Best wishes
Alcohol poisoning is serious business. Someone who is too drunk can vomit and not be able to protect their airway, and can inhale the vomit and die. At this point, you don't need to see a doctor, since you are feeling well and have cleared the alcohol from your system.
When it comes to drinking safely, there are a number of things you can do to avoid this situation in the future. They have tables you can print on a card that show how much alcohol is dangerous based on weight and sex. Google "Blood Alcohol Concentration %BAC Guide" to see an example. Drinking slowly helps, since it takes a certain amount of time for the drink to hit. Eating something beforehand/having food in your stomach is a good idea, since it slows down the alcohol absorption. Drinking plenty of water is critical, because alcohol screws with water retention mechanisms and makes you pee a lot, dehydrating you.
You are okay for now. But in the future don't drink so much. This is called alcohol poisoning and you can die from it. Please if you do drink again, do so moderately and learn what your limit is. - My limit is 1/2 beer, after that my nose gets numb.