Getting things done with a fussy baby

Hi guys, My LO is 6 months this week, she’s going through a terrible sleep patch for the past 6 weeks and is teething so it’s been rough. During the day she is also incredibly fussy, will sit for less than 5 minutes before whinging/crying. We use teething gel and calpol when her teeth are particularly bad but it doesn’t change things overly. I’m finding it very very hard to get things done, anyone else? She has always had to nap in the sling or be in the move in the pram. But aside from that now she has to be entertained constantly and held in the carrier. I can do bits like the dishwasher; put a wash on and cook the dinner etc. but beyond that I feel so lazy like I’m not achieving anything. I spend most of the day walking about outside or in my house. How are others finding this phase? Anything that helps apart from baby wearing? It is useful mostly but I don’t feel able to do lots of things when she’s on the front of me and it’s getting tiring! Thank you!!