Small aircraft single pilot reported an NMAC while flying from a non-towered airport to a nearby towered airport. There had been no communication on UNICOM prior; other than the position report. The other aircraft had executed a go-around due to the close proximity.

Narrative

I announced on ZZZ UNICOM that I was departing Runway XX to the southwest to ZZZ1. I departed ZZZ at XA:40. Just after takeoff I heard Aircraft Y reporting 19 miles to the southeast for Runway XY. I continued to monitor UNICOM until I was approximately 10 miles to the southeast of ZZZ. I switched to ZZZ1 Tower. At XB:00 I noticed Aircraft Y off to my right and 300 to 400 ft. above me. It was close but I didn't take any evasive action. I continued to ZZZ1 and landed. The Tower had me call them on the landline and advised me that Center had called them and wanted my registration number for the aircraft. They told me that the incident caused theAircraft Y flight to go around. I never heard Aircraft Y ever make any other reports on UNICOM while I was on the frequency. I was not on UNICOM any longer when I saw Aircraft Y pass overhead; nor was I required to be as I was clear to the southwest. I am submitting this report so that you can have my input into this incident. I don't have any suggestions as to the best way to remedy this situation so it does not occur again.