Yes, looks like hives for sure. Assume anti histamine has calmed it?
Does she have any other symptoms?
You'll need to go through your GP to get an allergy referral, this may take months, so make a note of the exact things she ate and the dates and the symptoms as well as you can before you forget. Well done on taking the pictures as they will also help.
Also, ask her to describe what she felt when eating milk (bear in mind it could be something else....though sounds like the milk).
Read this: https://www.anaphylaxis.org.uk/fact-sheet/cows-milk-allergy/ so you are clued up before facing your GP - they aren't always so well informed about allergies.
You can also talk to a pharmacist about while antihistamine to give her and how much.
And yes, keep her off all cow's milk (though, maybe all animal milk) until you have seen an allergist. Tests for allergies are usually skin prick and blood tests. However, neither actually really prove the presence of an allergy. The best way to do that is the eat or touch the thing you are allergic to. In this instance, I think she has proven her body is not happy with something (likely milk). Allergic reactions are really variable depending on the processing of the foodstuff and how much is consumed, as well as environmental factors so it will be hard to predict what reaction she might have to having milk the next time. There is no way to predict the reaction.
Sadly, milk is in a lot of stuff, so it is not a fun one to be allergic to. And, at age 8, she might not grow out of it. However, it is totally doable and realistically, in the current climate situation, it's not a bad thing (yey for vegans who mean milk free products are easier to find!). But, you will need to see a dietician if the allergist suspects milk allergy as you will need to make sure she gets plenty of iodine, vitamin D, calcium, etc. that is easier to get if you have regular cow's milk.
Good luck and try not to stress.