You could not be in a better position.  You already have the skills, it's just a question of quantifying them.  I really like the teaching experience.  We spend a lot of time educating our stakeholders.  Sure you may need some analysis experience with respect to eliciting requirements, writing use cases and the like.  We can take care of that with a little training.  I would suggest you take a look at the IIBAs carrier assessment t guide and compare your own experience to that.  This will give you a starting point.

I am also IT student, You have 10 years experiance in IT as a Business system analyst and project manager. you working on contract basis it doesn't matter. I think, you can find  agains business analyst opportunity.  If you interesting in teaching then you also do this side by side as part time for daily 1-2 hours. I hope you, you get a job in better company.