Questionnaires can be useful but many time the results can be inaccurate. For a vata/pitta type it would really depend on which dosha is aggravated vata or pitta. Generally, for you I would imagine sunflower oil would be a good choice. Sesame oil is balancing for vata and aggravating for pitta. Coconut oil is balancing for pitta and aggravating for vata. Sunflower seed oil is balancing for pitta without aggravating vata.
What would be possible bad reactions for sesame oil? That is very difficult to say as pitta reactions can be very varied but typical pitta aggravations include acne, tendency to be obsessive/compulsive, possible anger issues, feeling of heat in the body, redness, hives, itching, inflammation in any part of the body and many others. In extreme cases, a pitta aggravation can become drying and completely dehydrate the body and seem more like a vata vitiation (especially in a vata/pitta individual this is very possible). It is very hard to say without looking at a specific case, are you having any health complaints currently?