Resignation acceptance letter, experience letter, FNF statement, last salary slip, shall suffice to be as good as relieving letter. Peruse and new employer shall understand it, and accommodate you.
Relieving letter is issued post all settlements and signifies employee has been relieved after settlement of all a/c, and there seems to be nothing pending at your end. Relieving letter has become a custom. Work experience/service certificate is to be issued which your employer has agreed to supply however after a long period of 45 days and your drudge is that without this you are unable to secure employment and you are in dire need of funds.
You have given 5 long years to the company. HR/line management might be declining due to some internal policy. You may submit gentle representation in writing addressed to the good offices of your appointing authority, MD, Chairman, Company secretary and highlight 5 long years of association, meritorious service record, sickness of your wife requiring you at her side and remaining unemployed due to this and need of new job and employer's demand for relieving letter. Hence request to supply these at once. Employer might become strict but there is a difference between being strict and being stone cold /inhuman. If nothing works you have the option of raking up the issue under SE Act applicable to your state, and with O/o labor commissioner. The wages of the employee should be paid on last day in office or within next 2 days.
The mediclaim policy issued by employer is valid up to last day in office. Whenever you can you may obtain mediclaim policy covering your family and keep it regular. It provides additional tax relief up to Rs.15000/pa under sec. 80(D). Specified diseases are covered under 80(DDB). If you keep your policy in force you can be covered up to age of 80Y.