Doctors are human beings, too. That means that they carry personal opinions and prejudices regardless of precise information. Fancy degrees from nice schools don't necessarily make a person infallable.
Think of your body like a car. Cars need brake fluid, transmission fluid, antifreeze, gas, oil, and lots of other things. Your body needs vitamins, minerals, amino acids, proteins, carbohydrates, fats, and lots of other things. Being a vegetarian (or in your case, a pescatarian) isn't necessarily unhealthy or bad for growth; it just requires you to be a lot more conscientous about what you eat. Fish, beans, nuts, dairy, and fun products like seitan, tofu, and texturized vegetable protein can more than help you sufficiently meet your daily protein needs.
The recommended daily amount of protein to consume on a 2,000 Calorie diet is one third (in grams) of your body weight (in pounds). If I weigh 150 lbs, then I need to eat at least 50 grams of protein. I'm willing to bet that you probably consume more than 2,000 Calories a day though, since that much is consumed by doing nothing and sitting around. Try to get a healthy amount more than 1/3.
Where vegetarians really suffer is in getting the amino acids that the body is unable to make on its own. To do that requires a very diverse diet. This mostly applies to vegans, since diary, fish and eggs are all excellent sources for lots of amino acids.
One thing to watch out for is egg yolks, which have a very unhealthy amount of cholesterol. When you can, try to just eat the whites. Some yolk every now and then isn't a bad thing, but just eating two eggs a day can make your blood pressure sky rocket.
Don't worry about how skinny or heavy you are - just yet. Young people are known to have much higher metabolisms than older folx. Lots of the Calories that your body uses go towards developing your girl parts
redface and growing taller. Us old timers typically grow wider XD If you don't mind, go to this link and calculate your
Body Mass Index. That'll give you a lot more information than just assessing your own appearance in the mirror. If your BMI is lower than you want it to be, then start eating more. Rice, peanut butter, beans; anything that's high in both nutrients AND Calories.