Masters

Yes you can pursue from AFMC Pune, The admission in Maharashtra courses are based on rank obtained in NEET PG exam. Hence apply for NEET PG first. The eligibility criteria of Maharashtra course is given below. Eligibility criteria : Bachelors degree in Arts/ Science/ Commerce/ Engineering/ Technology/ Medical/ Dental/ Pharmacy/ Agriculture or any other professional courses from recognised Indian universities.

Admission in AFMC Pune in MHA course is based on ranks obtained in NEET-PG. Hence you have to apply through NEET-PG. The eligibility criteria for MHA is given below.
ELigibility criteria : Bachelors degree in Arts/ Science/ Commerce/ Engineering/ Technology/ Medical/ Dental/ Pharmacy/ Agriculture or any other professional courses from recognized Indian universities.

Are you asking for reappears?

The following are the available after completing B.Sc. Nursing for PG courses.
1. M.Sc. Nursing
2. MBA in Hospital Management
3. MBA in Pharmaceutical Management
4. M.Sc. Clinical Research
5. M.Sc. Medical Sociology
6. PGD in Public Health Management

PGD in Health Science is one year duration program in English medium at Annamalai University(DDE). The eligibility criteria is given below.
Eligibility criteria : i) A pass in MBBS/ BDS/ Paramedical Sciences/ Nursing. Orii) A degree in Psychology / Sociology/Applied Psychology/ Clinical Psychology or Social Work. Oriii) A degree in Management where Hospital Management or Health Systems Management is a subject.
So you are eligible for this program.

SPJIMR does not offer 5-year integrated management (Bachelors+Masters) programmes.

As per the Information bulletin for UGC NET December-2019 Annexure-V ( List of PG courses and their codes), You may choose Master of Hospital Administration (Maharashtra) Code No. 19 for paper-2. Please read information bulletin https://ugcnet.nta.nic.in/WebInfo/Handler/FileHandler.ashx?i=File&ii=18&iii=Y.

A candidate who has passed B.S.W. / B.A. degree examination from under a recognized university can see MSW admission. A candidate who has secured a minimum of 50% aggregate marks in B.S.W. / B.A. degree under a recognized university has the required MSW course eligibility.