Can I resign without a notice period if I have not signed the employment agreement letter?

Dear Sir/Madam, I was a physiotherapist fresher and I joined my company in March on 3 months probation period. However, I only went for orientation for 1 week in March and then fell sick so I was told to stay at home for 2 weeks due to fear of it being COVID-19. I was to be part of a new venture of clinics and due to COVID-19, the clinics did not start up in March as per schedule. Then the nation went on lockdown so I was staying in a rented apartment without a job for almost 2 months. So in March, I received a 1-week salary and after that, I was not having a job until 2nd week of May After the lockdown, I was asked to join again and it has been 3 weeks since I started working. I want to give a resignation as the location of the clinics and the work timings are not as per what I had been told in the interview and I am spending 60% of my salary on daily travel and the management is not ready to offer any help and told me to relocate to a PG near my work. I have not signed the employment agreement which states that a 1-month notice should be given and I wish to leave without giving 1 month-long notice period as I cannot afford to stay in Bangalore after all the transport expenses. Please could I receive some guidance? I want to be professional but the company has not delivered on their part and is exploiting the fact that the location of clinics was a verbal agreement and not written in the employment letter