Can I sue a hospital for giving me a wrong diagnosis?

You can sue, but suing a hospital is a very expensive and traumatic process. No lawyer is likely to take your case on contingency, i.e. on an agreement to get paid only out of what he or she can recover for you, because the cost of preparing and presenting your case will be much higher than the dollar amount you are likely to recover if you win. In short, though your case may be a liability winner, it's a money loser. Thank your Texas legislature and Supreme Court, and while you're at it thank the insurance companies and your fellow citizens (juries who buy the insurance company line) for making it impossible for malpractice victims to get justice in the vast majority of cases.