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No Mathematics and Physics are not compulsory in Graduation to apply AFCAT. However, Mathematics and Physics are compulsory at class 12th level with a minimum of 60% of marks for Flying and GD technical branches.

The eligibility criteria of M.A Psychology of Osmania University is given below.
Eligibility criteria : Must have obtained a Degree with 40% marks or equivalent CGPA with Psychology as an optional at B.A. / B.M.R.
or
Must have obtained a Degree with 40% marks or equivalent CGPA with Psychology in M.Ed. / M.A.(Education) / M.Sc. (Home Science) / Diploma in Child Psychology or Industrial Psychology.
Because you have not mentioned about the subjects studied at graduation level, So your eligibility can not be confirmed. However on the basis of yours PG degree you are not eligible for M.A Psychology of Osmania University.

It's upto your preference. M.Com from IGNOU would be more beneficial rather than M.Com from SOL.

Hello Saitanvi, oh yes. You can definitely think of pursuing a career of counselling psychologist after completion of your graduation in engineering. After becoming a graduate it's what you are mind dictates and what you feel happy in should be the field that you should choose. There are plenty of courses in psychology which you can pursue for which basic eligibility is graduation in any branch. Best wishes to you.