No, you don't have to use the first one.
You just have to wait until the time printed.
Edit for clarification:
The FP has 2 important things on it.
1. The time window during which it is supposed to be used.
2. The time when you can get another FP.
These are not necessarily related. You can normally get a second FP when the time window for the first has started, or 2 hours after you got the first FP, whichever is sooner.
So if you get a FP at 1:00 pm and the return time is 2:00pm, you'll be able to get another FP at 2:05pm.
But if you get a FP at 1:00pm and the return time is 7:00pm, you'll be able to get another FP at 3:00pm.
In either case, the time you can get a second FP will be printed on your first FP