I was offered a job a few months back and I took it without negotiating salary or looking elsewhere. I have not started my job yet and my first day will be in three months. Now when I see my colleagues(at my uni), it seems that I am the lowest paid among my colleagues. A lot of people have been contacting me for an interview and I have been denying them. Should I go for an interview with these people and then go back to my new company with their offer ? Should I wait a few months before interviewing with these people ?
Even if you loved the pay and benefits the delay between you accepting the offer and starting work is very long. Unless the contract has a penalty on them if they change their mind, I would as the start date approaches keep some level of job search going.
The risk you face is that if the week before your start date they say "oops we no longer need you to fill that position", you have no income and no recourse. So having applied to other positions means that you can quickly jump on any interviews.
Deciding on the timing on when you change from applying; to accepting phone interviews; to in person interviews - is up to you.
If you do happen to get a non-conditional offer that you are ready to sign, then you need to decide if you want to reject the first company. Please read all the documents that you were sent to see if there are any penalties you face by rejecting the first company.
Regardless of outcomes, an interview is always a precious experience in professional life: you sneak your nose in other companies, have a look at the people, see how they communicate, perhaps learn a new way of conducting the interview itself. All of this without talking about salaries, benefit, not even the actual job.
I suggest to accept and go to as many interviews as you can, even if you are already actively employed: just don't break rules, e.g. disclosing confidential info regarding your current position. Sometimes the option zero is handy --> silence.