How can I find out if I am a beneficiary of my uncle’s estate?

Since you mention an executor, I will assume that your uncle had a Will.  Accordingly, if you were a beneficiary you would have been so notified (at least once the Will was presented for probate). It's the law.  To check, once filed you can go to the Probate Court in the county where your uncle resided at the time of his death.  At the time of filing, it would have become a matter of public record and therefore can be viewed by anyone (for a small fee).      

You should be aware however that some assets can be transferred outside of probate.  For example, any property held as "joint tenants with right of survivorship". In such a case, the other joint tenant would have received your uncle's share in the  property by operation of law (automatically).

Note:  If you uncle didn't have a Will then a "Personal Representative" would have been appointed by the court .  They would act in the same capacity an an executor under a Will.  Accordingly, state intestacy laws would control the distribution of his estate.  Typically, the first to share in such an estate are the surviving spouse, if any, and the children of the deceased, if any.  If none, then to brothers and sisters.  In order for you to inherit, there would have to be no closer living relatives.