In these days of
unrepentant greed commitment to shareholder value, it is regular policy for airlines to sell more tickets than they have seats on the plane. This is because they know that statistically some number of people will not show up for a flight.
Usually this works out fine, because the expected number of people do not show and they can accomodate everyone who has a ticket.However, rarely, not enough people fail to show, and then they have more people than seats. If you do not have a seat assigned you, then you are one of the people who is at risk of being 'bumped' in this case.
If there are seats in any class then usually they will upgrade someone to make space in economy. It may be you who is upgraded or it may not. You won't be forced to pay extra. However if this isn't possible, then you will be offered some (usually substantial) compensation and a seat on the next flight. Be aware that if regular economy is full (which it is in your case) then premium economy will probably fill up quickly too.
It is likely that this will not be a problem. But if you want to be sure, your only real option is to buy (now!) a ticket in a class where you will get a seat allocation, i.e. Premium, at the appropriate price.