You just started gymnastics last week? I wouldn't be worried at all that you can't do a back bend yet. It is a more advanced skill than handstands and cartwheels so give it a bit of time.
Work on your bridges and rocking back and forth over your shoulders in a bridge. This will help increase the flexibility needed for a back bend. I would also recommend practicing back bends over an octagon so you can practice them safely.
One of the tricks to backbends is learning to stretch up as tall as you can before you go back. You don't want your head to go back first. I usually teach backbends going onto an 8-inch mat, and once they can control it onto an 8-incher, they can move to floor. A lot of kids don't understand how to push their hips over their feet while going backwards, and so they fall back too quickly and hit their heads.
In any case, I hit my head a lot on backbends on floor, and I've done gymnastics for 14 years. LOL, it hasn't prevented me from doing a lot of things.
i actually just taught myself backbends...it took about a month, but its worth it
I just walked my hands down the wall until i was in a bridge....every day...twice a day
and i held bridges for 10 seconds at a time
and tried to rock back on them
as i got closer and closer to doing one, i put an object (like a stepstool) that was about 6 inches from the ground and tried to c if i could do it then...
then, once i could, i put down books (4 inches from the ground, then 2)
and then one day i realized i could do it!
I dont know if it will take u that long, and i cheated and skipped some on some days, but for the most part i did it everyday
and for banging my head, I put pillows down sometimes but mostly did it on a really soft carpet without socks on so i wouldnt slide
also...try not to bend ur arms the second they touch the ground...try to lock them if u can- then u wont be able to hit ur head cuz ur hands will prevent ur from falling
sorry if that was really long and covoluted, but i hope i helped