While there's no doubt that birds that have some kind of impairment can function and take their place in the flock very successfully, all I had to go on was the description giving by the original poster, and with just that information I just don't see that happening with this chick. It sounds as if the injuries are far more serious, and if the OP is counting on the other chicks to teach this one what she needs to know to survive, I'm afraid she's going to be disappointed and the chick will likely die a rather miserable death from chilling or starvation or both. If I'm wrong, then that's a plate of crow I'll happily eat!
Okay, as for what to use for making a frame....lots of ideas here, as @bruceha2000 and others have said. Hardware cloth can certainly be used and bent into a suitable frame...just run some dowels through the holes at the very top and then press the hardware cloth down to rest on them so it can handle the weight of the chicks on top, especially as they get bigger. Tomato cages have been cut down and "smooshed" to the right height. Open wire shelving, @aart uses a cooling rack, someone even used an barbeque grill grate. Those are as smooshable, but by cutting off the legs on the shelving and then attaching adjustable legs, they can work just fine! Use your imagination, and if it works, great - if it doesn't, regroup. Nothing about MHP (except the need for a pad that stays on continuously) is set in stone! We work with what we have.