Is it sufficient for me to perform the Eid prayer with the people of my country, even though it is a day later than the rest of the Muslims, or should I forgo it?

If the people of your country rely on the legal sighting [of the moon], then fast and break your fast with them, based on the saying of the Prophet, peace and blessings be upon him: "Fasting is the day you fast, and Eid al-Fitr is the day you break your fast, and Eid al-Adha is the day you offer your sacrifices."

And if your madhhab (definition) (school of thought) requires that Eid be for you before their Eid, then conceal your breaking of the fast, and pray Eid with them as a make-up prayer on the following day. Do not openly show disagreement to avoid discord.