Why are you vegan due to a medical issue, I have never heard of such an issue that would require such a diet change??
Eating a vegan diet is against all evolution, and our bodies are not well equipped to thrive on such a limited diet, I can't understand how you could put on weight at what you claim to be eating, there is not enough food there.
You are probably suffering from malnutrition, and making yourself sick, lacking important fats and nutrients in your diet.
If you truly had zero fat in your diet your hormones would shut down, you need essential fats to keep hormonal function.
You need at least 0.5 to 0.85 grams of good fats per day for health reasons, so at your weight you should be looking at 30-40 grams of good fat per day.
Then you NEED protein.
I think you need to educate yourself in nutrition before embarking on a vegan diet, and if you must follow a vegan diet you must ensure you get your essential nutrients, and your essential protein and fat, the only thing that is not essential are carbs.