See if you show yourself as a fresher, there is no need and point of BGV.
Let me explain you the concept of BGV.
If I am recruiting an experienced person, (obviously he'd claim more than a fresher), i need to know if s/he's worth the pay s/he has claimed. How do I do this? By asking his current/former/previous employer(s).
What do I want to know from them?
How was your work? Were you productive? Since when are you working? What was your pay-scale? What were your major contributions? Recomendations.
If your past employer says (for whatever reason) that he was not satisfied by your work, the application in major organizations are rejected.
However if I am appointing a fresher, seldom companies ask for references for BGV. Even if they do, they accept your professor's references to know more about you. I am sure you can share your concern with 1-2 of the Profs who knows you personally and ask them what to do. Ask them if they can help you with BGV.
Otherwise there is no other way to find out if you've worked elsewhere before. We would get to know about your working history only if you disclose, only to the extent you mention. After all, we are only humans and who would know you personally to think you betrayed by hiding this 3.5 months tenure.
Apart, this is the practice. No one would disclose such short duration on their resume/career timeline. It really don't give an impression.
Hope it helped.