A no-bill means that the Grand Jury decided that was not sufficient evidence to send your case to District Court for prosecution. While a Grand Jury can turn around and change its mind and issue an indictment, up until the time that the statute of limitations time period runs for that offense, that is extremely rare. There will be a record of your arrest, the charges being filed and the no-bill on your record unless you obtain an expunction. An expunction cannot be filed until the statute of limitations runs. Apparently someone has advised you that it is 3 years in your case. Understand that the 3 years is from the date of the alleged offense, not from the date of the no-bill.
With background checks being standard in our computer age, an expunction is certainly a recommended procedure to completely clear your record. Once an expunction is granted, all records are erased and you are legally entitled to deny you were ever arrested or charged. An expunction must be done properly to ensure that everyone that has a record of the charges (police, FBI database, TX DPS, District Attorney, Sheriff etc.) removes them.
Right now, until you get your record expunged, it shows that you were arrested for the felony offense, and that a grand jury returned a no-bill - meaning not enough evidence for the case to be prosecuted. You are not a felon. You do not have a felony conviction. You have not had felony probation or deferred.
I agree with Mr. Ball, you need to speak with an attorney to seek an expunction of the arrest. Hopefully, the District Attorney's Office submitted the proper data to the Texas Department of Public Safety - Crime Records Division to notify them the grand jury declined to indict. However, many prosecutor's offices may not have the time, training or inclination to follow up on this important detail. You can obtain a copy of your criminal record from the Texas Department of Public Safety through their website. Do this so that you can have a record. Some of the private databases may not have this information, and accurate information in your possession may help you in a many different situations.