There is a notable difference. In both your examples, I would use "endlich". You use "endlich" when you couldn't wait for something. The emphasis is on the fact that you had to wait too long for it.
Endlich ist Wochenende!
Es klingelt. Das muß Thomas sein. Na endlich!
The word "schließlich" can be used if you describe an event when the emphasis is on the completion of some process and the outcome was not predictable. Yet, "endlich" kann still be used in place of it.
Ich habe lange überlegt, welches Auto ich mir kaufe. Schließlich/Endlich entschied ich mich für XYZ.
In the preceding sentence, "schließlich" is IMHO better, because the duration of the decision process was determined only by yourself, and there was no waiting. But in your example with the gold medal, "endlich" seems better, because external factors influenced the long waiting time.
Note that both words have further meanings that have nothing to do with what we have told about: "endlich" can mean "finite" like in:
Die Menge der geraden Primzahlen ist endlich.
and "schließlich" can mean something like "after all":
Wir könnten mal ausschlafen. Schließlich ist Wochenende.