I don't really understand this:
oil = hairloss
no oil = dryness
something else = dandruff
It sounds to me as if you need to start again with everything. Most people don't oil their hair. I do now and then, maybe once a week, but it's not dry in between.
Are you sure you have dandruff?
What does this mean:
"I do have dandruff as there are pimples on my face due to them." ?
I've never heard of someone having pimples due to dandruff, possibly due to oily hair...?
There are plenty of dandruff shampoos without oil, so maybe if you're sure it's dandruff use one of those (not H&S, it's horrible), then use a nice conditioner. Then look into your skincare routine and use a cleanser morning and evening.
You could take fish oil capsules, they are good for dryness.
Then you need to think more about the hairloss - I doubt oil is causing it. Maybe your diet? I had bad hairloss when I had a problem with my gall bladder, due to lack of nutrition - iron can cause it, so maybe take iron (and you'd probably need to take vit C with it) bt that needs to be a long term thing.
What 'type' of hair do you have, is there anything else that could be causing hairloss - stress, over styling?