Only read the OP...
Right firstly congratulations on your newborn.
Secondly - give yourself a break!
Don't put pressure on yourself to be perfect, there's no such thing as a perfect parent!
Your baby is a teeny tiny newborn. All they will want to do all day and night is breastfeed. This is completely NORMAL. They are building up your milk supply and they also need the physical contact.
As someone who used to work in HV i can tell you with complete confidence that the HV does not care two hoots about you're house (unless it's actually unsafe/unsanitary and by that I mean bags of rotting rubbish, extreme damp and electrics etc!)
I would always tell new mums that actually, a spotless and showhome house was often an indicator that the baby wasn't being prioritized- your HV expects muddle: washing up stacked up and piles of laundry! So chill on that front.
Gammy eyes - again normal. Try rubbing a few drops of breastmilk onto them (yes really).
Next you need to adjust your expectations. The first 3-4 months are all about getting to know your baby, establishing a milk supply and meeting your baby's basic physical and emotional needs (Google the fourth trimester). You will probably spend HOURS a day sat on the sofa breastfeeding.
If you have a partner then shower when they are home and they can pitch in with tidying/cleaning and prepping a packed lunch for to keep in the fridge overnight.
Set up little 'feeding' stations around your house and task your DH with keeping them stocked with up with bottles of water, fruit and cereal bars. Then if you get stuck under a feeding/sleeping baby you will still have food and drink.
Definitely try out slings - I liked the close caboo ring sling.
And above all, don't put pressure on yourself to 'do everything'. As much as you can try to rest and recover from the birth and being pregnant. You have a lot of healing to do and if you're making breastmilk it really takes it out of you. Your priority is your baby.
The website kellymom is also good for any breastfeeding quieries (it reassured me that cluster feeding for about 7 hours straight was normal!)
Good luck