Allergic reactions?? Or something else

My baby has been breaking out like bad. Went last week and said it was a heat rash. Went back today and said it’s like cradle cap but all on her face neck and head since it was nowhere else. But we got home and my boyfriend took her outfit off because he thought she was hot and but her in her bouncer...Well we have a cat and I had to chance him out of her bouncer a couple of times.. and now her back is breaking out too.. 1st two pictures are yesterday. The other 3 are from a week ago.