But I should wait for it to sync up right?
No. You can back it up while it is synchronizing, and should do so as soon as possible.
All the stress came because I wanted to back up my wallet in the first place and keep it all safe before going to sleep. Now I have to wait days until I dare use my computer again.
You can shut down Bitcoin Core (previously known as Bitcoin QT) while it is synchronizing. It will remember where it left off with the synchronization and when you start it back up again later, it will continue synchronization from where it left off.
I used it yesterday for firefox and firefox is acting weird so I decided to let it sit until it's syncs up.
If you have malware on your computer, then the bitcoins could already be stolen. It is important to be certain that the computer you are using to access your bitcoins does not have any malware on it.
Thanks a lot. I can finally be normal again. I wasn't human these last days because the guy who sold me the coins didn't say anything reassuring at all
I'm sorry that you've had such a bad experience. I'd suggest taking the time to learn a bit more about what you are doing before you put any more money into something that's going to cause you so much stress. Note that bitcoin is still an experimental technology. It is extremely high risk. You shouldn't put money into bitcoin that would be devastating to lose. While there is a lot of potential that the exchange rate for bitcoin could be significantly higher than it is today, there is also a substantial rick that you could wake up tomorrow and discover that the exchange rate has dropped to less than $1, or that some new bug is discovered that makes bitcoin worthless.
and I read some posts that said that addresses are lost with encryption, I don't really know what that means.
Bitcoin Core pre-generates the next 100 addresses that it will use and keeps those hidden from you. When you request a payment (or generate a bitcoin address), bitcoin gives you one of these pre-generated addresses, and then when it gets a chance it generates a new address to replace the one it gave you. When you encrypt the wallet, it discards those hidden pre-generated addresses that you have not yet requested from the software and generates new ones. If you want to put your mind at ease that your Bitcoin Core still has the address that you had the bitcoins sent to:
Choose "Receiving addresses..." under the drop down "File" menu.
You should see the address listed along with whatever label you gave it (if any).
As long as you see the address here, your wallet still knows about the address and will be aware of the transaction as soon as it catches up with synchronization.