The short answer to your questions is yes, you can take too many vitamins.
What you have heard is true, that if you take water soluble vitamins they will pass through your urine and you will rarely have any issues overdosing on them. The vitamins that can cause issues are the fat soluble vitamins - vitamins A,D,E, and K. These are not passed in the urine, and can build up in your body to dangerous levels - but you usually have to take A LOT of them before this happens.
For vitamin A, you need to be taking more than 33,000 IU a day before you will get any adverse side-effects.
In terms of vitamin D, you run into problems when you are taking more than 60,000 IU. The recommended max amount of vitamin D to take per day is 4000 IU.
Vitamin E's upper limit is 1100 IU.
Vitamin K overdose is hard to come by, and there is actually no documented upper limit as it is extremely rare.
So yes, you can overdose on vitamins. however, you have to take a lot of them before you'll develop any adverse reactions. In terms of the vitamins that your health adviser prescribed, if your health adviser is a licensed medical professional I would go with their opinion.
The best thing to do though, is to go see your family physician
or a dermatologist
regarding your "skin disorder". They can fully assess your problem, and decided on the proper treatment [whether it be vitamins or other medications] that you'll need.