What you're describing in the nappy area sounds like thrush/yeast. If you can get an antifungal cream, that should help a lot. Try to keep the area as dry as you can for now to keep more yeast from growing. Not sure if you can get infant probiotics where you are, but that can help, especially if she's been on antibiotics more than once already (kills "good bacteria" in the gut and allows yeast to overgrow.).
The rash on the face could well be an allergy, but not for sure. If the diarrhea has been happening a lot, it may be something she can't tolerate yet - not necessarily an allergy but an intolerance. Dairy is a VERY common allergy, but soy, wheat, and eggs are other common foods that can cause reactions. Tomatoes can have a lot of acid, as can some fruits, so I'd go easy on those (they also have sugar which can aggravate yeast). Why do you think squash? It could be, although squash is usually toelrated well.
How does she react to carrots and greens with the rice? You might be able to expand her diet that way, especially if she can tolerate some mild seasonings. Mine were happy with a little cinnamon for carrots and for squash; curry powder also goes well with those. and greens like spinach and broccoli went well with both yogurt and cereal, so if she's eating pasta & rice you can try pureed spinach with either of those like a sauce? Green beans too - they're more vegetable than bean since the seeds are so immature.
