There is no such thing as a "permanent" work visa. After receiving a degree, you may work on OPT for a year. You would then need to find an employer to file for an H1B; that takes care of 6 years.
If there are no willing and qualified US citizens or current legal residents wanting the job, an employer can file for a green card on your behalf. However, you meeting the requirements will be difficult as there are many librarians -including a family member with a BS from an elite school, a MS in a technical field, work towards a PhD in a technical field, a MLS, AND more than 10 years of experience in well known libraries who is currently looking for new job (and has been for a year now) - looking for jobs.
I would not even hold out much hope for you getting an H1b sponsor since libraries work on very little funding. Just finding someone to file the paperwork will not work. They must actually employ and pay you.
Realistically, your best option is to go home as you promised you would when you originally obtained your F-1 visa.

