But if you do not have a license to carry in IL, you also cannot carry "on your person" in TX. You can have a firearm in your car. But not your pocket.
Not going to speak for the OP, but if he has a permit from another state (several states issue permits to non-residents, including my state of Arizona) he can, in fact, carry in TX as long as the state he got his permit from has a reciprocity agreement with TX. Of course, I don't know if he does have one or not, but I'll give him the benefit of the doubt.
In Arizona, we have "defensive display" law. It hasn't been tested in court yet, but basically it allows us to attempt to diffuse a situation by showing that we're carrying. I'm not sure I would go that far, as it could make the situation worse, however, it is legal in some jurisdictions.
Exact wording of the law:
The defensive display of a firearm by a person against another is justified when and to the extent a reasonable person would believe that physical force is immediately necessary to protect himself against the use or attempted use of unlawful physical force or deadly physical force.
In my CCW class, they said that the wording of the law said you could "display" your firearm (it would have to remain holstered, as actually drawing isn't covered) if a reasonable person would believe that you were about to be attacked with physical force. It doesn't have to be deadly force. You cannot draw unless you believe you are in imminent danger of death or serious injury. Having said that, in a case like that, an LCP might not be a deterrent, as much as something larger. But then again, don't think I would "display" my gun as it would give up a potential tactical advantage.