Is there a reason she was on the sensitive stomach food? I know that Natures Variety makes a limited ingredient food, if your concerned with things that are common triggers for bullies & their allergies. It honesty will be a trial though, you may end up going through a few until you find the one. We had to go through several kibbles, and finally decided kibble wasn't for us, so now we're on The Honest Kitchen (one of their bases) and we add in our own protein. Usually a lean beef, turkey, or kangaroo.
The dry nose could be related to weather changes.... You can apply a bit of coconut oil, or Aquaphor and it should clear up. We also had a nose issue, and ended changing Tyson's water to filtered water, it cleared up great, but he will still get dry nose during a drastic weather change. Do you get Stella any probiotics? This could also help with getting a more consistent poop, and will also help with any belly issues This is the one we use, and I purchase it off Amazon.
Lastly, Yes you definitely need to do a slow switch, esp if she has a sensitive tummy. Start out by mixing a very little bit of the new food in with the old.... and slowly over the span of about a week (7-10) you should be fully switched over. You can also add in a little plain jane canned pumpkin to help with the transition. Please do the transition, not just a cold switch - it will be bad on her belly