We had similar and we think it might be silent reflux, which is where they swallow whatever liquid is brought up from the stomach so you don’t see them spit up. Check the symptoms and see if she has any of the others! If so, you can get gaviscon or omeprazole prescribed, which seems to have helped our little boy.
My baby is same age and he has been diagnosed with GORD and CMPA. It all started 5 weeks into kendamil milk, started projectile vomitting, then screaming started for over 14 hours a day and this is like serious screams like it sounds like someone being murdered. The NHS are not that great at dealing with it so you have to persist if you do feel it's an allergy. It also gets worse as time goes on. He also had diarrhea and blood in his poo and even more recently black bits in his poo. The other bits are sneezing, coughing when feeding and dry flaky skin. He's now on amino acid milk and omeprazole and seems to be doing ten times better. They don't do any skin prick testing so it's basically switching milk to hydrolised or amino acids via GP or hospital dietician or cutting dairy out of your diet if your BF.
To add to that dairy takes 4-6 weeks to leave a babies body so don't expect immediate changes it's a very long process
The back arching is definitely a sign of reflux. If she doesn’t have any skin issues or like green mucous in her poo it’s probably not an allergy. They don’t test them until much later anyway, so if you really think it might be an allergy the next step is an elimination diet. Most people start with dairy - you’ll need to cut it out of your diet completely for at least two weeks to see if it makes a difference. Other common ones are soy and gluten. You’ll only want to try one at a time though. Mine has confirmed CMPA (dairy allergy) and we’re seeing a specialist privately to make sure it’s not the really bad kind (she had wheezing/hard to breathe after feeds when I was on dairy). If you have the money you can always go this route as well