No you are not allowed to bicycle on the Freeway.I don't think that is true for Texas. I know that I have ridden quite a bit on I-10 and the cops riding by paid me no mind. I have had lots of cops pass me by so if it is illegal (which I doubt) it isn't well enforced. I found I-10 to be a good way to go for some of my crossing of Texas. That said I do think I'd consider using US 90 more of the way if doing a ST again.
In Louisiana and eastward, interstates are off limits, but in Louisiana enforcement is spotty on that. One cop there told us we'd be OK but advised that we get on and off at ramps to avoid bridges that usually didn't have a shoulder. He had stopped us when we entered the state by bike. He said it was illegal, but gave the advice above when we asked about a better route. We didn't take his advice since there was a nice secondary road that paralleled the highway and we used that.
West of Texas on the ST I think we rode on the interstate some in all states we crossed except California and I think it was legal in all cases. For sure cops went by and didn't bother us.
There may be specific sections of interstate there that are posted as off limits.