You should probably go to the doctor to rule out anything serious. If you are otherwise healthy, then examine your diet. Have you started eating a new food with your diet? Maybe you are having a reaction to a specific food so you can try eliminating anything new until you find the culprit.
This is an indication that you developed an allergy to a type of meal and that is what is causing the rash. You need to avoid some meals to see if the rash will disappear so as decide what it is that you are allergic to. However, you will still need to see a doctor to get a good remedy for the rash.
Good job about your transition into vegan lifestyle! Possibly an oil you are cooking with... best to uncomplicate your meals & wait for it to go away. Then every week add something. Some people are allergic to coconut oil/milk if you recently changed to that or soy!