What did you do in your gap year? Do you have any AP credits or dual enrollment credits or community college credits? UNM has a political science major http://degrees.unm.edu/undergrad_programs/386.
36 credits for the major, you need 26 credits to transfer in.
If you go to a CC you could transfer and maybe do this degree in a total of two years?
UNM is one of the worst state flagships in the country. If you want to get out of New Mexico, now is your best chance.
If you really have to get out of New Mexico, you could apply to the University of Alabama at Huntsville. You’d qualify for a full tuition scholarship (even though you took a gap year). It will automatically be given upon admittance to the university. I go there and I love it, but then again I’m in engineering 
I agree Alabama is a good option. Your choices are so very limited, and Alabama would be a good school that is away from home. Please consider something that you can realistically afford.
OP would have received a Woodward or Presidential scholarship at UNM had he/she attended last year. However, both scholarships apply the lottery scholarship first and then these school scholarships pay the difference. My D attends UNM on a Presidential scholarship. The Lottery Scholarship paid $4600 of the $8000 Presidential this year, so those freshman scholarships are no longer an option since the OP took a gap year and can’t get the lottery money now.
D is in the honors college and really enjoys those smaller classes. She lives on campus in beautiful new housing and had a great freshman year with pretty great professors overall. I don’t feel that her education there was bad in any way. It’s a shame that the OP took a gap year and missed out on a free college education. I can see why the parents don’t want to go into debt over something that could have been free.
Having said that, I would recommend the OP attend UNM as it is much more affordable. Having a large debt for a sociology degree is not wise. The OP will then need to take out even more loans to attend grad school in order to make that degree worthwhile.