You CAN garnish a bank account before judgment, but only under particular circumstances.
You should be able to find an attorney that can listen to your questions and explain it to you for less than $100. If you call the Houston Bar Association, I suspect that you can find an attorney who will listen to your story and answer your questions for even less than that. Be aware that any kind of suit like this will run you more than $1000, and probably triple that.
I'm not your attorney; my answer to your question includes assumptions. If you want me to be your attorney, I'm easy to find.
1st you file a lawsuit. 2nd you litigate the suit. 3rd you win a judgment. 4th you execute on the judgment, which can include levying a bank account, or wage garnishment, or attaching personal or real property.
The time frame varies, since if the defendant fights the suit, it can take years, but if they don't, it can take only weeks.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
I am not aware of any avenue that is available for freezing the funds of a party to a lawsuit prior to the time of final judgment, other than in a divorce case.
Rather than trying to get answers to generic questions like this from strangers, I suggest you hire a lawyer and pose them to him or her. The law is complex and there are few reliable pat answers to generic questions. Your lawyer will be able to give you reliable answers tailored to the facts and issues of your case. This, in my view, is what you need.