Was I nearly involved in an accident?
No, you were not nearly involved in an accident. 

If the flight crew is ready to go, an Airbus A320 takes about 40-50 seconds from the moment take-off clearance is given until lift-off. As soon as the aircraft is off the runway, the next one can land. On some busy airports, 60 seconds between take-off clearance and the next landing is a daily occurrence.

In 60 seconds, there is a lot that can prevent an accident. For example, ATC could instruct the incoming aircraft to go around should the departing traffic not be ready to take-off. This is quite a normal event which happens every day at busy airports around the world. In such a case, the aircraft ready for take-off would have to wait for the incoming traffic to pass overhead. It sounds like you may have experienced such an event. 

Here is a video of something similar happening in Birmingham.

Since it is a 'normal' event, there is no central database that tracks these issues.