We'd love to help you, but this is a hard question for anyone to answer over the internet with more than guesses.
It's not generally a problem on a vegan diet with protein or iron. The things that tend to be the lowest are Vitamin B12 and perhaps Omega 3 and iodine and calcium, although this various. You may want to look at these at some point, although it's fairly unlikely that any of these are the cause of the immediate issue.
Nutritional deficiencies can take a long time, months or years, to develop. It may therefore that after 15 days your dizziness was due to air poullution or the weather or not drinking enough.
It could be psychological, if you worry about the change of diet might have negative effects, then maybe it will. If you think positively about your avoidance of animal cruelty, you may be more likely to have better health!
It could also be something related to trasitioning from one diet to another rather than the funadmentals of the diet, but the body adjusting to a change.
Make sure you are eating healthy foods, not too much junk, and get the basics right, little alcohol, no cigarretes, some exercise, good enough sleep, drink enough water, stay indoors if very hot/cold outside, and limited stress, for example. And give it some time.
If it's a minor issue, perhaps it will go away.
However...Please do use your own gut instinct here on whether you should be going to the doctor and if unsure better safe than sorry.