I can sympathise with how you feel as I've been in a similar position for a few months. I left my well paid job where I didn't really have to think too much about what I was spending my money on when we moved to the US. I'm expecting our first baby in a few weeks.
The first couple of months were hard as I was just randomly asking DH for cash for groceries, clothes (needed mat things), money to have coffee with new friends. And I felt shit every time I had to ask. Losing my financial independence sucked!
But we sat down and worked out a system where he gives me cash every 2 weeks that I use for groceries (I write a meal plan so I stick to what we need) and then the rest for me (and baby). I have my own bank account which I put some money aside in so I can save up and buy him things like birthday presents etc without him knowing!
If I need to get a lot of baby/house things in one go I'll fill up an Amazon cart with it, check he's got enough cash in bank and use his card to pay for it. He pays for my phone, all bills and most petrol directly (I fill up the car if I need to). We also do a big monthly bulk-buy shopping trip.
I frequently remind myself that this is our money and not his!
Ideally we should get a joint account for all this but the system works at the moment. We might revise later once we've got our heads around the US banking system.
Oh and I call my fortnightly money my wages by the way as that is what it is. I'm running the house, cooking, cleaning and about to have a tiny human to look after too. Actually I think I need a pay rise...