Well, earlier this year when my oral meds just stopped working, my Doctor put me on Lantus. I want to tell you that, that was the onset of my sweating just as you described. I suffered extensively from night sweats and would soak the bed and in the morning after my Lantus shot, I couldn't get enough air conditioning. Up until I started the insulin, I'd never had a problem.
BUT, (there's always a but) the longer I was on Insulin, the more the sweating subsided. Now Im on Byetta and I haven't had a sweating episode since, but yes, I had exactly the symptoms you described!!!