Having worked in Clarks for mannnnyy years some of the comments on here I disagree with.
You do not have to wait a month from walking before getting shoes. Although it IS true that children cope very well bare foot and so parents needne rush out for shoes.
I find it really sad that shops like tesco and asda can sell shoes to parents with no idea... but I equally recognise that fitted shoes are a luxury some cant afford.
Its almost impossible for someone who doesnt know how to fit shoes to buy a pair online for their child and have any idea if they are the correct fit.
I have never seen a 3yr old with size 4 shoes. The only explanation is some form of foot deformity??
In this instance - with no access to a trained fitter in a shoe shop I would suggest taking measurments of her feet and using an online guide to see what that equates too.... I would then choose the absolutly softest pair of footwear you can find ( im thinking firm soled slippers!!) And use them untill things calm down and you can get her measured.
When you put a shoe on her you are looking for a thumbs length gap at the end for growth, when the shoes are on her feet sit her on a seat/step and gently tug them - they should stay put and not slip around the ankle. When she stands make sure the straps and the ankle suport dont cut in to her ankles and especially the bones found each side that stick out a little. You should also have enough width in the shoes that her skin doesnt bulge out.
Watch her walk them, she shouldn't trip or her feet turn in (unless she does this anyway)
Pick up a 4. 4.5 and a 5 from a supermarket when doing your weekly shop and try them at home with the above advice.
Good luck x