Hi Edoardo,
No problem. Let me try to clarify my thoughts a bit more, before answering your question about why GRE.
Looking at the title of your post, I had a feeling that you have not really understood what GMAT is testing you. GMAT is not an academic test - neither math test nor English test. It is a testing of executive reasoning skills. So yes, a solid academic background will help, but that does not translate directly into a high GMAT score. GMAT requires you to strategize your problem-solving approach, use logical reasoning, integrate different data formats to draw inference, and make decisions under time pressure, with all kinds of traps idiosyncratic to GMAT. You may or may not have been exposed to these skills in your undergraduate study.
Secondly, I think your expectation for the preparation time is unrealistic, which many had pointed out. Going through your post again, I found that I kind of overlooked a piece of information - you took IELTS. That means your undergraduate institution likely did not use English as primary instructing language. This could potentially be a reason for your lower Verbal score, and that will in turn impact your DI score, given that even some native speakers will feel time-pressured in DI section due to the large amount of information presented.
All those are not to say it's impossible for you to achieve a desired GMAT score. But you need to have the right expectation/mindset, seek more structured prep method, and put in more efforts than you imagined.
As to GRE, obvious we don't know much about you, being just friendly strangers on the Internet. But sometimes more academically-oriented students will perform better in GRE than in GMAT, thus the suggestion. Not sure if there is free GRE practice test out there. If yes, I guess what I suggested is to give it a try and see which test you would feel more comfortable with, and therefore enables you to score better and gives you more advantage in graduate school application.
Just my two cents.
EdoardoMarz
First of all thanks!
Can I ask why like you many people are suggesting me to try the GRE?
Is it because they test different skills or they have a different structure?