My question involves civil rights in the State of: Texas

I was convicted of a Class C felony in 1984, arrested by border patrol, and was convicted, served 4 years probation, which ended in 1989. I have never tried to buy a gun since. I have heard that in Texas, it is legal for a convicted felon top own a gun, but not to carry it outside the home. I( have also heard that in TX this is limited to pistols, and shotguns/rifles are OK.

My question is, will I get in trouble even trying to buy a firearm? I have run background checks on myself, and my felony never appears. Perhaps this is due to the fact it is a federal offense.

What are my rights in this case?