I suggest you look at the TX Board of Nursing website. The information on there is easily accessible and tells you quite explicitly what their requirements are. Why haven't you looked at it before now? I would have thought if you were serious about moving to Texas you would have been researching this for quite some time (unless you just decided very recently, that is.) If you had looked into this in any detail you would have seen that there is no possibility AT ALL for a non-USA trained Mental Health nurse to get an Authorization to Test (ATT) for the NCLEX-RN from the TX BON. You can't just take the exam, you need authorization to do so from the BON once your credentials have been evaluated from CGFNS and have been deemed comparable to a USA educated Registered Nurse. Being deemed comparable to an American RN means your educational transcripts must demonstrate you received xxx amount of hours in both clinical & theory in Medical & Surgical care of the neonate, child, adult & geriatric patient as well as obstetrics & maternity nursing, and mental health too. Clearly your transcripts will not show this as the curriculum in the UK for mental health nursing does not cover most of these 'generalist' areas.
You will either have to return to university and do another degree in Adult Nursing at a university that has a dynamic curriculum whereby the Adult Nursing programme includes OBGYN/paediatric/mental health hours (mine did fortunately), or you will have to find some way of 'making the hours up,' an almost impossible task since you will have so many hours to make up and even then you will still be a registered Mental Health nurse. I am not trying to be discouraging just presenting you with the facts as they are. If you have been thinking of moving to the States for some time now, you should have known all of this already. The immigration process is complex and getting to the point where you have a visa in your hand and you are flying out to the States to start work will entail a lot of research, hard work, exams (yes, plural, not just the NCLEX), expense, stress and time (several years.)