You must correctly identify the edition and the printing. A first edition can undergo multiple printings. The first printing of a first edition can be very valuable while a later printing of the first edition can be worth very little.
Many sellers of books throw around terms that are incorrect (they don't know) or intentionally misleading, to drive up the price.
So if you don't know how to identify what you have, you'll need an expert.
You can start by looking inside at the first few pages for a copyright date, the publisher, and any indication of the printing. A later edition will usually not say 'second' or 'third' but give some other name to it. For example, 'The Cambridge Edition'. This would be a dead giveaway that it's not a first edition, and most likely not the original publisher.
So take what you find and look for it on eBay or ABE books. Look for the closest match you can find, and then, look at actual sold results, not asking prices, which are often inflated. I do not know if ABE books shows results.
If you should see what you have selling for good money, then it's time to have an expert look at it, to confirm that you have a valuable book.