In the "My account" area, you will find the "My events" and "Purchases and receipts" tabs. In these modules, you will find a summary of your registrations, purchases and payments.
If the registration appears in "My events", everything is in order.
You can also check that you are on the list of participants for the event in question. To make it easier for you, you can search by name (note that some events do not disclose a start list).