You sent $10 to an exchange, instructing them to send BTC 0.0016 to an address.
If you look up your transaction
3f624c15d2479ac6aa696b7357fcb650bf29d442f1a980a65488da3bd9501a48 in any "blockchain explorer", for example here, you'll see this transaction had 2 inputs and 20 outputs. I guess this was an exchange from whom you purchased $10 of BTC and asked them to send it to
1D3HZXK8So3n6LahCGWpkAxbQ3P6br1gSs, the exchange probably combined your transfer with other people's to save transaction costs.
One of those output addresses was the "account" you mentioned.
1D3HZXK8So3n6LahCGWpkAxbQ3P6br1gSs. It received ~$10 in this transaction. Note that this is a Bitcoin address not an account number.
But you don't own that address.
However the $10 of BTC sent to this address is now marked as spent. Three hours after your transaction, it was moved to address
19d1iU8XvYAdPVbCKHExD8hNqbC7T7NwW5 along with 22 other inputs.
The earliest transaction for your address was April this year. From what you write I suspect you did not have control over this address that long.
It could be that addresses
19d1iU8XvYAdPVbCKHExD8hNqbC7T7NwW5 are both owned by some business (not by you) who swept the $10 and other small amounts into a different address for privacy or other reasons.
You mention "account" and "earnings" and seem confused. These are strong indications that you are the victim of a scam.
It is safer to hold Bitcoin in a standalone wallet, not in a hosted wallet run by a website. Many websites are fraudulent, especially any that promise high earnings (or any earnings at all). It is important to take care to investigate any website before sending money to one. Do you know the names of the people who own the business? Do you know when they first registered the domain name used by their website? Do you know where their business is based? Can you check any of this independently from them?
A scammer may show you a web page that makes it look like your $10 has grown to $20. They might encourage you to invest more. If you ask about withdrawing money they might tell you about a withdrawal minimum amount you didn't know about before, they might say you need to send a withdrawal fee or some other fees. They might try to trick you with watch-only wallets or other deceits.
The business running the website you opened an account with might be legitimate. We can't help you much with your relationship with them. A legitimate business will have a support telephone number or other way of contacting them and resolving your problem.
What to do
I suggest you forget about your $10, at least for the next few weeks. Spend some time learning how Bitcoin works, why it is high risk, why it is very hard to earn any money with Bitcoin investments in October 2018, how various scamsters operate, how to choose a wallet, how to backup a wallet and private-keys, how to test recovery from your backup actually works, how to make sure someone you love gets your Bitcoins if you are run over by a bus tomorrow (20-30% of all Bitcoins are lost forever).
No private-keys, no Bitcoin
This is a common saying. It means, you own no Bitcoins if you don't know your private key and don't know for absolute certain that no-one else knows your private-key (e.g. by having known your wallet's old password at any time in the past).