If you are an independent adult, preferably living away from your mum, I’d think you can. Just like anybody else who might want to adopt them – and assuming they’ve not been snapped up as puppies in Shelters usually are.
By ‘giving them their signature’, I assume you mean your mum signed them over to the Shelter? As she’s most likely the sole owner of the puppies you wouldn’t have been involved in the signing over.
You’d have to expect a Home Visit just like anybody else – and if you live at home with mum, that could be ‘awkwards’!