It appears that you had jumped the gun by tendering letter of resignation. You had done this on the strength of "offer fitment" and not "Offer Letter" per se. When one receives a letter clearly specifying when one should join, then only one should resign. Your anxiety is increasing as company could leave you in lurch.
In the last paragraph, you have written that "Also I called HR few days back , she saying offer letter has been put on hold for first week of april, meanwhile you can search for other option if you get the same the its your career. she said once we get approval for offer letter we will surely contact you". This is a clear indication that company's hiring decision could go against you.
Without getting anxious further, start searching for the job. Now your liability of serving notice period has come down. Any company will be more than happy to take on board a candidate who is ready to join at short notice. Turn this adverse situation to your advantage.
All the best!