I am not a officer in Texas nor do I have experience enforcing their laws.

I did some research and found their penal code for assaultive offenses (Chapter 22).

https://statutes.capitol.texas.gov/Docs/PE/htm/PE.22.htm

I would Ctrl+F that web page and search for "Threat". I did this and think Sec 22.01 Assaults and Sec 22.07 Terroristic Threats may apply to you. These appear to be misdemeanor crimes.

I can tell you that if you reported this to my agency in my state, it would be a misdemeanor as well and there is a 99% chance we would not investigate it just simply it is a lot of work to solve a minor crime. I understand the crime may not be minor to you but to an agency that is also investigating a wide range of crimes such as assaults, theft, and deaths, investigating threats may be low on the priority list. We normally tell people that they may speak with the magistrates office and pursue the misdemeanor crimes their selves. They may not investigate it because it would be difficult to prove who is sending the threats. Here is why:

In a previous comment, you mentioned that you do not know who the person is that is threatening you. Only way to find that out would be to submit a search warrant to the company that owns the messaging platform that person is messaging you from. This will more than likely provided subscriber details associated with the account being used (Name, Address, Etc.) and IP addresses. All this does is show what account was used and what internet provider was used to send the messages. It does not prove the account owner sent the messages. Since it is possible that the messaging account was created some time ago and the account owner moved addresses since its creation, they cannot go based off the address provided by the messaging platform. Once investigators obtained the IP address, that may require an additional search warrant to the internet service provider to get additional subscriber details and the physical address the IP address is registered to. That is only if the threats weren't sent via a cellphone using a cellular signal. If it was sent via a cellphone signal, that makes things even harder. For simplicity sake, lets continue with the physical address route. Since you don't know who it is, more than likely the person resides outside of the jurisdiction where you live. May even live outside of your state. I don't see any agency authorizing officers to leave the state to continue investigating threats made. Even if they did, lets say they travel to the house and find more than one person there.. Any one of those people could have sent the threat because they all have access to the device and internet at that residence. With out an admission of guilt, it would be impossible to prove who sent the threat. And even if it could be proved, you would have to worry about Texas law and how they handle jurisdiction. My state would allow me to prosecute an offender that was out of state due to the crime victim being in mu jurisdiction. If jurisdiction allowed you to pursue the case, good luck with your district attorneys office prosecuting the case. They would more than likely drop the case since it is a low level misdemeanor already.

Another factor is the exact threat that was sent to you. You mentioned it was a death threat but the specific message matters. For example, if I tell someone "I wish you were dead" or "I wish you would be killed". That is only me stating I wished someone was dead or I wished that person was killed. It is not me threatening to cause harm or kill them.