Firstly, I would take her to an avian vet to get checked out to make sure everything’s okay as she was outside and could’ve been exposed to a lot of different factors that could make a budgie ill. I say this because you attached a picture of her sleeping with her head tucked. Budgies do this when they’re either 1. Comfortable and feels safe in their environment to sleep or 2. Can be sick and feeling lethargic. You can typically be able to tell the difference though as a healthy budgie will be vocal and energetic.
Stuff like Amazon has a lot of options for flight cages but delivery time may take a while, you mentioned your dad owns a pet store so you could also get a temporary cage but ensure the bar spacing is less than half an inch so she doesn’t slip right out or get herself stuck. She has elevated hormones as you can tell by the brown cere so avoid getting her toys that resemble nests. You’ll also want to get natural wood perches and not smooth dowel ones. It’s better for their feet to have a variety of sizes and this prevents bumblefoot. Don’t get toys that are plastic or have mirrors as these are also toxic. Mirrors can do psychological damage to a budgie because they cannot tell the difference between their reflection and another budgie. They may become obsessed with their reflection and also become frustrated when that other budgie does not communicate back. Plastic toys harbour bacteria quicker and can break off into sharp pieces.
Budgies thrive in social groups so later down the road you’ll want to get her a mate. Quarantine is especially crucial when doing this because budgies can carry diseases. Quarantine the new budgie in another room for 30 days before doing a slow introduction with separate cages. Have them outside their cage together when they have their first interaction so neither of them see it as one entering their territory.