I got married to an American Muslim (new) in an American court by an official without any witnesses. Is this marriage islamically legal?

The Nikah is not valid.

A Nikah is performed with a proposal (Iejaab) by the male or female and acceptance (Qubool) by the male or female in the past tense and in the presence of two male Muslim witnesses (Hidaaya vol. 2).

It is Sunnat that the marriage be announced and performed in the Masjid and the bride be represented by her Mahram (father, brother, etc.). The bride gives consent to her representative (Wakeel) in the presence of two witnesses to perform her marriage at the Masjid. At the Masjid, the Wakeel represents the bride in the presence of the two witnesses and the stipulated dowry. The witnesses must be two trustworthy and pious male Muslims who are not her ascendants e.g. father, grandfather or decendants e.g. son, grandson, etc.

The Mahr (dowry) is the woman's right and should be stipulated prior to the marriage.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai