So first I tried the trial version of Diablo III with an account. When I upgraded to the full version, all of my quest progress was lost, I had to start all over again. Is this normal, or is there way to restore my progress?
Did you make the purchase on the same account? Sometimes it happens that a person may accidentally be logged in on the wrong account when making their purchase.
The fortunate thing is that Trial accounts can’t get too far in on Diablo 3, and you should be able to catch up with your progress fairly promptly.
If you want to still find the account then customer support can try to help you find it, https://eu.battle.net/support/en/help