There is no wait list at most of the schools in Texas but... If you don't get in one semester you have to reapply every semester until you get in. So you could get in right away - or it could take awhile. Some schools in other states run a wait list so that people don't have to reapply, there may be some here that do that as well, but I personally am not aware of any.
Whether you get in or not depends on how many qualified applicants there are applying for each available seat. Your chances of getting in can vary from one semester to the next as well. If there are 100 seats available and 600 people apply and out of those, 100 of them are 4.0 gpa's and fully qualified otherwise with whatever the school requires, then you'd have to be right up there with them to even have a shot at getting in.
Some schools base admission solely on GPA, others on a point system, others on a combination of things including gpa, test scores and interviews.
You need to check with each individucal school you are interested in and find out what their recent applicant pools have consisted of. In addition I would advise applying at more than one school and possibly considering taking pre-reqs to meet a future BS to help open some other options up for you as far as the number of schools you can apply to.
The reason there are not more seats available in nursing schools despite a nursing shortage is that there is also a shortage of nursing faculty. It isn't as simple as just hiring more professors, the money to pay them has to come from somewhere. Nurses working as professors do not earn near as much money teaching as they would earn working as an RN. Some hospital systems such as THR are now using their own nursing staff as faculty for in house nursing programs
for their non-nurse employees who would like to become nurses and running their own nursing programs AT the hospitals in partnerships with local colleges. I wouldn't be surprised to see these kinds of programs become more common in the future.
Just explore all the options, and do your research - it's not impossible, even though it may sound that way sometimes!