If you did consular processing abroad, the embassy will have pasted a visa into your passport. This is a “one time use” visa – when you use it by entering the USA you become a “Lawful Permanent Resident” (LPR). This is called “activating your status. If you have paid the Green Card fee as instructed by the embassy, your plastic Green Card usually is sent to you about 2 to 3 months after initial entry. However, if you have to travel out of the country before you have the plastic card, you can use your one time use visa again. Upon activation it will have been “endorsed” and can be used for travel for up to 1 year after the initial entry.
So, if you have already activated, you are an LPR. However, airlines don’t always understand the rules. In that case you might want to print out this guide which describes the documents in detail. Have the guide with you at the airport. Page 40 of this guide has information about the endorsed visa.
I hope that helps.