It is true that Israel's creation was immdeiately followed by a war. This is known as the First Arab-Israeli War. The war began after the end of the British Mandate for Palestine and the Israeli Declaration of Independence. Such tensions began after the adoption of the United Nations Partition Plan for Palestine. However, the territory was eventually invaded by Egypt, Transjordan, Syria, and expeditionary forces from Iraq. The fighting lasted roughly 10 months, with several periods of truce.
The Arab Israel war, or the first Israel war was fought between the nation of Israel and the Arab nations that opposed its creation. Israel was invaded by five Arab nations
The answer really depends on which of the 13 Southern states you are referring to. Each state issued their own Ordinance of Secession, in either 1860 or 1861. Hope this helps.