I’m graduating in 2 months and realized at the beginning of the year that I am in the same boat. I started taking product design classes here at my university so just get as much exposure to design as I could prior to graduation.
From what I have learned so far I would say the major differences between mechanical engineering and ID are process and ideation. Thinking like an ID is VERY different from thinking like an engineer. You need to explore every possible solution to a problem, good and bad, because even the bad solutions can lead to your best solution.
Engineers like to come up with a solution that solves a problem and stick to it. Designers come up with multiple solutions that solve the problem in different ways. They also tend to include much more of a human element into their solutions.
I’m probably missing something, but you get the point. They are different schools of thinking. My best advise would be to take classes at a local university if you can. Read design books, sketch, bring out your creative side. My current design professor is having us read “Design Thinking” by Nigel Cross. So far it is a great book.
-Greg