Vitamin D plays a vital role in helping your gut when you are celiac or gluten intolerant as it has been found to play an important role in preserving the mucosal barrier.
Now you have been diagnosed as being unable to eat anything containing gluten, it is important to take some kind of multivitamin supplement because your body is not able to absorb the vital vitamins which are in food. As with all thing of a medical nature, you should consult your physician before taking supplements as they will be able to ascertain which vitamins you need to take and which dosage.
Gluten-free products are often low in vitamin D, iron, zinc, magnesium, B vitamins, calcium and fiber so it is important to ensure you have these vitamins included in your diet gluten free diet. When you have been newly diagnosed, you will probably find that you are vitamin deficient due to the way your intestines have been (mis) functioning, so it is wise to begin ingesting vitamin supplements soon as you can, again consult your physician.
You should also be watching your cholesterol levels too. In your life before having go gluten free, your cholesterol levels may have been very low. This is more than likely due to the fact your body was not absorbing any of the cholesterol you were eating. So now your tummy is getting better because you are eating the foods which are right for you, you may find that cholesterol is now being absorbed, so just keep an eye on it.
I take vitamins B-6 and B-12 but I do try to include the food groups which these vitamins are found such as spinach, brown rice, avocado, potatoes, chicken and salmon. Of course, whole grains and wheat contain these vitamins, but hey ho, I can not eat these but there are plenty of other foods I can eat which contain them.
These unfortunately on their own do not provide all the nutrition I need, mainly due to cooking processes, even though I do try to steam anything that can be steamed! So I have to take supplements too.