I agree that unless there is a physical reason, then it is not normal to need to rest all day at 38 weeks. (I worked up until the birth, every time, and we all hear the stories of "nesting" where women clean out the top cupboards, and move all the furniture around on the day before labour starts.)
If you are lolling around in bed/on the sofa, unable to get up, it is probably because you are depressed, or have a mineral deficiency, or similar. Not because you are pregnant.
So get to the GP.
Your DP/DH is telling you not to worry about it, but it doesn't sound like he's helping much. If he has just left for work, he's had two days to help you get the house spic and span. Is it? Thought not. So, he is part of the problem. He needs to be saying things like, let's just tidy this, and then we can both sit down, for a bit. Not, oh don't worry about the house, just sit down. Talk to him about it. Don't be fobbed off with "don't worry about it". Tell him how important this is to you. Plan a way forward together.
You need some rules.
Allow yourself one mug, one plate, one bowl, one knife, one fork, etc. and the same for DD. If you need a plate, for example, and it is dirty, wash it up. You might also have the energy to wash everything else in the sink, as there won't be much there.
Every dish, pot and pan to be washed up within 24 hours of being used. If it's not cleaned before the next food preparation time, clean first, then start to prepare.
All food to be eaten in one designated dining area (the kitchen?). Once food is eaten, wipe down the table, and chairs and floor, if needed, immediately. Then it is ready for the next time it is needed.
Do not go to bed, even for a nap, without tidying any cups or mugs, or other food/drink detritus to the sink or bin first.
Get a big basket for DD's toys in the living room, and as soon as she is in bed, or napping, chuck them all in there.
Put a laundry basket in the bathroom. Put dirty clothes in it as soon as you take them off.
Do the cat litter as often as needed, seriously. (Is this once a day? I don't know, I don't have cats) Make a time when it is always done, and do it. As much as a pregnant woman should not be touching a litter tray, if the cat is going elsewhere in the house, then I think it's better to contain the problem to a tray, where you can use protective gloves, and wash hands well after. If the cat starts going any old where, you and your baby will be coming up against it all the time, without gloves, etc. Or get rid of the cat.
Think of other rules that will work for you.
Your house does not have to be a show home. It just has to reach an acceptable level of tidiness and cleanliness. By giving yourself too high a goal, you will always fail. You give yourself an excuse to fail. Change your goal from wanting the house to look amazing, to making it an acceptably clean environment to live in, and bring up DC in.
But first, go to your GP!