If you did regular probation on the Obstructing a Highway charge, this conviction stays on your record for the rest of your life. It doesn't drop off after 5, 7 or 10 years. It's permanent. This may happen in other states, but not in Texas.
If you did deferred adjudication probation on this charge, then you are entitled to file a Motion for Non-Disclosure after you have completed that probation. However, this order will only seal this charge and disposition from the public, it will not erase it from your record (so law enforcement will continue to have access to it). However, you were never convicted with a deferred, so you can absolutely deny a conviction, but would have to admit a deferred if that specific question is asked.
Typically in Texas, an Obstruction is offered as a reduced charge by the State when they think they may have problems proving the case against someone arrested for DWI. You may be eligible to expunge (erase) the records of your DWI arrest (since your record may reflect that if an employer is requesting arrests and convictions. However, be advised that under the current law, DPS legal department is opposing these kinds of expunctions (though there is a strong movement to amend the Code of Criminal Procedure this legislative term to close the door on this opposition.
Talk to a criminal defense attorney in your area to see if you qualify for any of the above relief.
Disclaimer: This answer is provided as a public service and as a general response to a general question, it is not meant, and should not be relied upon as specific legal advice, nor does it create an attorney-client relationship.
To add to Mr. Walcutt's answer, even if you qualify to have your record sealed, that does not mean that it absolutely will be sealed if you apply. You file an application in the court in which you served the probation, and that court must find that it is in the best interest of you AND the community to seal the record. If indeed you got a DWI, a court may be less willing to seal it.
If you got deferred, you have not been quote convicted of anything. However, many employers do not understand the difference and will consider that you were deceptive in answering the question. I usually tell clients, if they do not have time to move to seal or they cannot get their record sealed, to explain the situation (after they have reviewed it with me & I can help them put it in the best light possible) on the front-end so that it is clear you are not trying to deceive, and you can explain the changes (if any) in your life since the time of the offense. Nine years is a long time if you were a very young adult when it occurred.