The first big question is if you're public sector or private. If you are public employees then you do not have collective bargaining rights under Texas law which means there would be no union certification election or contract. This doesn't mean you can't take action and win changes, but it will not be easy and will require strong solidarity and militancy.

If you are private sector then you can go through the NLRB process if you choose, but you are not obligated to.

The big unions you would want to talk to are the National Educators Association (or a local thereof), The AFL-CIO (who will probably put you in touch with American Federation of Teachers), SEIU, or the Teamsters. If these unions were to work with you they would probably urge you to take less militant routes, but will have lots of resources that they might dedicate to your campaign.

Alternatively you could reach out to a smaller more radical organization like the IWW, United Electrical Workers, or EWOC that would be more supportive of radical action but wouldn't really be able to dedicate much to your effort.

Ultimately the resources a large union contributes mean very little to a union effort compared to the organization, solidarity, and militancy of the workers and their community though. All of the lawyers in the world will not win your demands. The best thing you can do right now is form a small committee of the coworkers who most seriously want to organize and interview with these organizations and democratically pick the one that feels best. Don't be scared of going independent either if your committee is unsure of who to work with or if these organizations refuse to work with you.