I'm not surprised if your sex life has suffered when you feel in pain or beset by hormones let alone during the early days of parenthood.
You actually want a sex life with your DH so I assume you have explained to him as frankly as you have here that you are not happy to go without?
He takes your lack of enthusiasm as a personal lack of interest and gets upset. Yet he knows that after the PMS and your week on, unless your eczema flares up you are liable to be a willing and happy participant?
I want to (fulfill his needs) like I used to be able to not in a way that demeans me in any way
Sorry can you elaborate, I don't think you mean manually or orally pleasing a partner in the absence of PIV sex is demeaning, are you afraid that he will cultivate a porn habit if you aren't ever-ready...?
At present you feel cheated because two weeks out of four you are not jumping his bones, okay so during the fortnight you are in the mood would it possible to arrange overnight care for DS so you and DH can have time away together?
I understand you hanker after the old days but for now you need to talk to him and where possible fix your health. You have to take responsibility for your health but the sexual area of things is a joint responsibility.
Without getting into defining rare or and how deprived is someone who enjoys sex three times a week for a fortnight, I would definitely go and see your GP and talk about your PMS. Also is there an eczema nurse at the surgery? Ask a GP for a referral to a dermatologist.
You might be advised to cut out certain food groups - dairy or wheat - ask about food allergy testing carried out as part of eczema diagnosis. An emollient my DD finds soothing is zeroAQS which she orders at the chemists, it's not on the shelves but they get it in for her.