Wow, ok! I didn't realise you were going to be over here so quickly. You posted only like 3 days ago about having received your passport back!
Definitely be nice to yourself!! You've not even had a chance to get used the idea of moving to the UK (let alone the time difference). I think your first post was less than 1.5 months ago-- so to have packed up your life and moved over at a moment's notice is kind of a big deal, and definitely wouldn't have been easy for anyone.
I had a long time to get used to the idea of moving to the UK (after doing a study-abroad in the UK, the boy I fell for and I stayed together doing long-distance for 3.5 years), I made the decision sometime around April, then moved in September. I settled in okay, since I came as a student which was a good environment to make friends. But I still remember one day, about a month in, I was in a Wilkinsons and had a bit of a panic attack while buying cleaning supplies, or something else that seems mundane.
It's stressful. There are similarities between the US and the UK, but there are many differences too. Brands have different names, or you're not sure which shop is best to find something, and finding an equivalent to something you couldn't live without in the US is damn-near impossible to get ahold of here. But I promise, if you give it a chance, it gets better.
Start with the basic essentials if you haven't already:
1. Stock your fridge/pantry-- if you can't fathom leaving the house right now, you can even order online and have them delivered to your door at a pre-selected time. Try:
Ocado, Sainsbury's, or
Tesco2. Register with a GP -- your post does raise some health concerns. If you continue to have difficulties, you will want to get it checked out. You will need to bring proof of residence, a form ID (your passport will serve both purposes), and proof of your address-- if your work is helping with your flat, they should be able to help with this also, if you haven't gotten any mail yet. Find GPs in your area here:
NHS Find a GP 3. Set up a bank account if you haven't already. This will make paying for everyday things much easier. (Won't run into the problem of having to withdraw cash from a cashpoint because the cashier doesn't understand how a US card swipes..). To set up a bank account, you'll also need proof if residence/ID/address. Some well known banks include: Barclay's, Lloyds, TSB, NatWest, HSBC, Santander. Just a note that if you have an account with Lloyds for example, you can take money out of any of the other banks' cash points (ATMs) without a service charge. Very few cashpoints charge you to take out money, unlike the US where you have to use your specific bank's ATM for any transaction to avoid fees.
4. Find your way around town. Last week's tube strike probably didn't make things easy for your arrival here, and another is supposed to start tonight. It is definitely a hassle, but not exactly the norm. I strongly suggest downloading the
CityMapper app for your phone. It has been a lifesaver for me more than once!
London is a massive city, which can be equally overwhelming. Take your time getting used to things-- like your neighborhood, the way of life you'll become accustomed to, and how you respond in these new situations/environments. Like you said, even the little things are going to be a bit different here. Growing up in the US, I never thought I'd be hopping on a bus to buy groceries, or plan ahead to do laundry (because each load takes 3 hours and even then isn't even fully dry!).
You've only been here a few days, therefore I do suggest you stick it out at least a few weeks. I definitely think you're experiencing the culture shock that comes with the idea of being more permanently based in the UK (which can be terrifying). Try not to stress and think "OMG, What Have I Done?!" Give it a chance; there may be things you can never get used to, but you don't know until you try. Personally to relax, I find red wine and bubble baths a great help
Best of luck to you-- Thankfully you've moved when the weather is a bit nicer and warming up (and staying bright outside longer), so at least it's that little bit less depressing!