Baby keeps falling and bumping her head from sitting position

My precious 7.5 month old girl learned to get into the sitting position a few days ago and has been loving it. Any time I put her onto the floor, she’s getting onto her belly, then her knees, then her bum. When I congratulate her, she smiles so big and gives herself a few claps (another skill she recently learned). It’s absolutely heart melting.

The problem is that she occasionally loses her balance and tips over. 90% of the time she’s fine— she’s great at finding her balance and catching herself with her arms when that doesn’t work, and also knows how to get back onto her knees/belly safely— but that other 10%, she falls. I’ve resorted to hovering around her and most of the time I catch her, but three times now I haven’t managed to get my hand under her head in time. Two of those times have been backwards falls which is obviously the worst because she can’t catch herself whatsoever.

The thump of her head on the floor followed by her cries is one of the worst sounds Ive ever heard. My girl has always been very sensitive to pain, the smallest bump sends her into tears, so these falls have been a nightmare. I cry right along with her. You can see in my post history when she was a newborn she would accidentally head-butt my clavicle so hard she would cry. So head bumps have been an ongoing issue for us/anxiety for me. My heart really can’t take it. And what if her head can’t take it! I’m absolutely terrified of this harming her brain and/or development😞

What can I do to prevent this?? We have a pretty thick carpet laid down where she has her floor time but this doesn’t stop the falling, bumps, or crying. I don’t want to get her the helmet because I’ve read it interferes with development in its own way. Is there anything I’m missing??