All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Adoption is one of the practices that existed in Jaahiliyyah (the Pre-Islamic Era of Ignorance) and Islam invalidated it and forbade it, and ordered that the child be attributed to his real parents.
Allah Says (what means): {And he has not made your adopted sons your [true] sons. That is [merely] your saying by your mouths, but Allah says the truth, and He guides to the [right] way. Call them by [the names of] their fathers; it is more just in the sight of Allah.} [Quran 33:4-5]
Your real mother is the one who gave birth to you, and if any another woman claims that she is your mother by mere adoption, then there is no consideration for her statement, and do not pay any attention to it. Being Mahram to each other is not established between you and her by this adoption.
If there is any dispute with her about this, then you may take the matter to an Islamic court or what serves instead in non-Muslim countries, such as Islamic centers.
For more benefit on the ruling of adoption, please refer to Fatawa 119119, 84422 and 82371.
Allah Knows best.