A credit card company can sue you in any state if you owe them money and default on your agreement. Indeed, buried in the fine print of most credit card agreements is a clause stating that the laws of the company's home state (usually Delaware) will govern any disputes.
Yes, they can sue you. The area in which Texas is almost unique is the homestead protection. If you own your home, they can sue you and attach a lien to the property, but cannot take the house to pay for the debts.