OK, here's something else you can try feeding. It might sound a bit off-the-wall, but might be worth a try.
If you can get other grains like oats or millet or brown rice or barley, soak them (overnight should be long enough) on the countertop, rinse them, cook them into porridge, and then puree and feed, maybe dilute with some of your own milk that she's used to - a different grain might be the best bet. Josie had awful "digestive issues" with rice cereal, but barley did the trick; Natalie did best with oatmeal and rice. Go figure.

The soaking helps the grains be easier to digest.
I'm actually kind of surprised about sweet potato, but that definitely sounds like an allergic reaction to me. And I hope this doesn't open up a can of worms, but are you feeding her commercial foods or home-cooked? Either way, you might want to try the other and see if it makes a difference. For example, if you're cooking in something that's been recently used to cook milk or eggs or in a bowl that's recently been used to serve them, that may be the issue rather than the food itself. Just a thought.