Hey hon, oatmeal, like rice is hard on little tummies. It may be best to try with some veggies or fruits to start with, since she has a sensitive tummy (and especially if the reflux is not well controlled yet). Sweet potato, pumpkin and pears are usually good for refluxers.
That being said, if it's just a few times I don't think she will seriously lack vitamins, here cereals are enriched with iron since after 6 months old it is considered that they need added iron, especially for breastfed babies.
Drs always told me reflux would lessen as they grew but it took a good while before it did. As of 10 months old we were totally med-free, I had never even hoped for that when he was 8 months old, so it will eventually go away, but 6 months is really young still. Usually it gets better once they start to stand a lot and be much more upright. Hopefully the GI will be able to help you.