There are many different ways to work in Immigration.
1. Law enforcement/detention
2. Legal - working for organizations such as RAICES that try to help relocated immigrants, among other things. https://www.raicestexas.org/
3. Working in Social Services, including at the detention facilities
While all immigrants aren't necessarily Spanish-speaking, speaking Spanish is almost required to get these positions. Not all positions will be working directly with immigrants. For example, you could be in charge of fund-raising, or managing a social media page, or trying to get grant funding to keep a program going. Attorneys might take on an issue, rather than work directly with a particular client.
Sadly, many jobs require degrees, and a 4 yr. degree is usually the minimum in social services. Law enforcement is normally a 2 year degree. Since you are in El Paso, I'd recommend looking at what this organization does, and seeing if you could volunteer. Volunteer experience always looks good on a resume! https://www.elpasodiocese.org/about-us.html