Recently I had to join this company for 4 month internship
So, you're saying, you were "instructed" to join this company? Most likely not, you chose to. During the time of the appointment, they would have mentioned about the compensation structure - why did not you think of the payout then? Same goes about the commute.
Reality is: It's a 4-month internship and usually the companies do not "expect" the interns to "deliver" much value to the organization, they are there to learn. So, trying to compare the compensation structure with that of a full-time employee (which you were before) is not correct.
I feel like I should re-negotiate because it's like I am doing job in the name of internship but I am not sure how this will turn out.
On what grounds? That they are making you learn? They are assigning the work for you to learn, it's not really their problem whether you are already experienced or not. You should have clarified those points during the internship application and interview - now it's very less likely that they are going to be willing to open a (re)negotiation, at all.
Given that you accepted the offer and now, by seeing the work pattern is known to you, you are feeling you are entitled to get more. Well, you will get more, once you complete the internship , get a degree and find a job.
Till then, you need to hang on.