In addition to the response by Sharmila ji, first, I would like to say that the actions taken by your employer were obvious because you never informed them about your illness. How can they understand the reality of your sickness and that a doctor has advised you to take two months of rest unless you inform them somehow? Bed rest does not mean you cannot make a phone call or send an email to your employer. Now, please tell us what you did.
Probationary Job Option
Second, can you please let us know who provided this probationary job option to you? You mentioned, “Now you are doing MBA.” Does this mean you enrolled yourself for an MBA after this working period (probationary job), or what?
If you were working in the past and have enrolled and started your studies after this period of working, there is no need to prove this past employment unless asked by your university, with whatever benefits/options that a student can expect. Therefore, you do not need to worry about losing your position for campus recruitment or listening to your seniors.
Consulting Mentors or Faculty
Third, if you are talking about your senior college mates by addressing them as SENIORS as quoted above, I believe you should not take them seriously. Instead, you need to consult a mentor/college faculty (someone you can talk to) or any college authority in this regard. Certainly, you should not take your college mates' beliefs seriously.
Relieving Letter and Employment Proof
Regarding the relieving letter, if asked, it is you who knows that you have worked for a family friend, not the university/college. You just have to prove that you were employed, not that your employer was a family friend or whatever. In this case, your relieving letter will certainly be sufficient, but what value your campus recruiter gives to the company of your family friend where you have worked is totally going to depend on them. We can't actually say anything in this regard.
Regards.