Note that you would have to obtain absolute proof that your birth mother is Jewish. Only if this is done can you be determined to be Jewish. I know of people who have evidence but no absolute proof of Judaism in the maternal line one or two generations back who have converted "misafek" (from doubt). Since the father was not Jewish, they avoided the problem I allude to below.
However, this would cause more problems unless you can also identify your birth father as well. The reason for this is that if you are a "child of an unknown father" anyone you want to marry could be a forbidden relative.
This only applies if the father is (or could be Jewish). A nonJewish father is not considered a relative (from the standpoint of Jewish law), nor would any of his relatives (who would convert) be considered your relative.
If you are not Jewish and convert, you can marry anyone (aside from a female convert being forbidden to marry a kohen)