1.Yes,if there is efficacious and alternative remedy is available then the high court doe snotossue prerogative writ.
2.if the Police did not register FIR then you should have filed petition u/s 156(3) CRPC fordirection upon police to register FIR.
3. If the police still sits idle then file writ petiiton agaisnt police inaction. For non registration of FIR the high court does not issue Mandamus.
4. So instead of preferring an appeal I would strongly recommend you to file petition before the CJM under section 156(3) crpc and then writ petition seeking report on progress of investigation.
5. Preferring an appeal in all likelihood is to meet same fate as that of the writ petiiton.