If it was a felony and if the charges were not dropped or reduced to a misdemeanor, then you will not qualify for a Texas CHL. What concerns me is the fact that you paid a "fine." That indicates a conviction, as you don't/can't pay a "fine" for anything other than a conviction. Now, you can pay other fees, such as court costs related to a deferred adjudication, but those aren't "fines."
Non-violent felonies, such as felony hot checks, will not disqualify you, but only if 1) you received deferred adjudication and successfully completed your deferral/probation period; and 2) it was not for a violent felony (TPC Title 5 "Offenses Against the Person" or TPC Chp. 29 "Robbery"). If the charges were not dropped, it is also quite possible that they were reduced to a misdemeanor.
As llwatson said, you need to get an official disposition sheet on this matter.
Good luck,
Chas.