You should get an attorney as soon as possible. If you asked for an attorney and the detectives continued to interrogate you, then the statements given by you during the interrogation may be thrown out. The facts regarding your case should be looked at by a defense attorney to see whether that is the case.
Many people think that because "they didn't read me my rights," that the case will automatically be thrown out. However, the Miranda rules (right to remain silent, right to have attorney present, and right to have attorney provided) are rules of evidence, which must be followed in order for a custodial interview/confession that follows to be admissible in evidence against the defendant later. Texas law (Texas Code of Criminal Procedure, Art. 38.22, Sec. 3) also requires, among other things, that for information obtained through custodial interrogation to be admissible in court, it has to be electronic recorded, and the Miranda warning must be on the recording before the interrogation, and the detained person must be on the recording waiving (giving up) his/her right to counsel.
One possible problem is that Miranda only applies in situations where a person clearly isn't allowed to leave. But a lot of police interrogation happens before the person is under arrest, and the police are clear that "you are free to walk out of here anytime you want." If the police stated that you were free to leave at any time, and you weren't in restraints, than it may not have legally been a "custodial interrogation," necessary in order to trigger Miranda. A good attorney would ask you several questions about the circumstances of the interrogation in order to tell you whether it was legal (or may be admissible) or not. If you call our office, we would be glad to give you additional information at no cost or obligation.
If you ask for a lawyer, they must give you one and stop questioning. Be aware that the question of what is "asking" can be a very complicated issue (I know it doesn't seem like it).
It is definitely an issue that you should look into. The burden is on your attorney to file the correct motions, urge the motions and put the correct information into the record. Evidence doesn't get eliminated from a criminal case without an attorney that handles it correctly.