Is there some form of legal document I need to obtain to prove that I am the executor?

I am sorry for your loss. Unfortunately, in addition to your loss you have received misinformation. A person may only be an executor if they are named as such in a Will. Since there is no Will, there can be no Executor. Additionally, an Executor is not actually an Executor until the Will is admitted to probate, the order is entered appointing the Executor by the Court and the Executor signs and has the Letters Testamentary issued by the Court. Since there is no Will, a determination needs to be made if the estate needs to be administered or if a set aside is possible. If an administration is necessary, you cannot serve alone as you are not a Nevada resident. Residency is required unless you were named in a Will. Since there is no Will pursuant to Nevada las you cannot serve unless you are a co-administrator with a Nevada resident. We generally recommend using a professional to do this unless there is an exceptionally honest person who is willing to dedicate the time. Both of you may be jointly liable for the acts of the other, so sometimes it is best just to allow the professional to serve. You state as the eldest child you are the person to be in charge. Under Nevada law all children are equal in terms of ability to serve, there is no preference based upon birth order. I am unsure why you want medical records, but that too requires a court order. Honestly you need to have a consultation, a one on one to in person or telephonic meeting to address the numerous issues you are facing so you may decide whether to employ counsel or continue on your own.

With no will there will be no executor. Any interested person, including yourself, can become administrator of your mother's estate to handle her affairs. You will need to go to probate court and file a Petition for Probate. This is a process that takes some time and can be complicated.

Because your mother was a resident of the State of Nevada, in order for you to act on behalf of her estate it is necessary to obtain a court order appointing you as the administrator of her estate. This requires filing a court petition in Probate Court requesting that the Court appoint you as the administrator of the estate. (Because there is no will, the position is technically called an administrator, rather than an executor.) In this situation where your mother did not have a will, you and your siblings are equally entitled to serve as administrator even though you are the oldest. Any of the three of you can file the petition requesting to be appointed as the administrator. Until you are appointed as the administrator, it is very unlikely that anyone will release medical information to you or provide you any access to or use of her financial accounts. Even though you live in California, because your mother was a resident of Nevada at the time of her death, it is necessary to file the probate petition in Nevada, and Nevada laws would apply (which are different than California laws). You should speak with an attorney whose practice is focused on probate administration to ensure that you and your attorney understand Nevada's probate laws and can help the administration of your mother's estate be as simple for you as possible.