Baby keeps falling and hitting head

My 8 month old is able to sit up and stand and walk along furniture etc. We are in the middle of moving so we are doing our best to have stuff baby proofed but it’s definitely not great but we try. The thing is, he will sit up and sometimes he’ll sit for 15 min no problem and then other times he will fall backwards after a couple of min and we have to set things up behind him just in case or sit behind him ourselves. Now that he’s standing and walking along EVERYTHING there’s been a few incidents of him straight letting go and falling backwards and landing right on his head. Luckily we have carpet but jesussss it’s exhausting. We are packing and cleaning like crazy with a deadline so it’s impossible to constantly stay behind him and help him, though we are there 97% of the time. But for instance we were just eating and he was crawling and in a matter of a couple of seconds after we took a bite of food he fell straight back again from standing position. He must’ve stood up in about 3 seconds and bam he lost balance. We literally cannot eat. We are exhausted and he’s extra grumpy and we’re (I am at least) at our wit’s end. I’m worried he will have serious brain problems or something bad will happen to him but I want him to learn as well to not let go but I don’t want him to hurt and aghhhh. Parenting is so fucking hard sometimes I feel like I can’t do anything and moving is horrible with a baby. Any suggestions? Will he learn soon? Is this happening to anyone else? We feel like terrible parents when this shit happens.

Some good news is he’s starting to talk and trying to copy us 🥹