Can changing the type of diaper you use give baby a rash?

We used Huggies for the first 4-5 months and then switched to Luvs because they were cheaper and we were in a bad money situation well we switched back to Huggies and I've been putting them on my baby girl for about 4-5 days and she just all of a sudden got a bad rash, the rash is only on her private stuff so I thought it might be something to do with the diaper switching.. with this info could that be the cause of the rash?

If you think it could be another reason please comment.. I change her diaper pretty often as I have the whole time I don't like her sitting in pee or poop. The only different thing in our life with her is trying baby foods but I didn't think that was it because it's only on her down there.