It's funny to read your post because I was pretty much in the same spot as you a "few" years ago. So you know what I did ? I dropped out ... I didn't do the 6 months internship ... And I'm still paying the consequences of that choice.

Finding a first job was a nightmare and I've been stuck in helpdesk for more than 5 years now. My advice to you would be to finish your darn Master degree no matter what. Whether you decide to complete it this year, or next, finish your degree. I'll add that the professional environment might be a welcomed change of pace and you might enjoy it more than studying, so go into the internship with a positive outlook.