In response to your question, allow me to cite the AAS policy on this matter. The ruling states that:
Double Master's degrees are permitted only when both are included
in the institution's original offer and both courses can be completed
within two years.
It may be in your best interest to choose, related courses located in the same university in this case. Though not specifically stated, a direct connection between the courses will best satisfy this requirement.
I am unnerved
This term is defined as to deprive of courage, strength, determination, or confidence; upset. I believe you chose the wrong word to describe your emotion. Perhaps say you were inspired instead? I am certain you did not want to use a negative term here.