Pls give newbie advice for hair problem

Hi,

I am north indian age 30, 5 feet 8 inch, male, currently staying in US, 70 kg, 5ft 8 inches.

I used to have thick hair. When I was 12-13 years old I had typhoid for approx. 2 months (relapse) that resulted in increased hair shedding for 1-2 years. I would wake up to find my pillow covered with 50-60 hairs. I would lose some during combing and shampooing. I had dandruff too and my head would feel itchy. As my hair density and thickness was still pretty decent, I was young and made the mistake of not paying enough attention to proper balanced nutritional diet and lifestyle. During college I had some thinning of hair and some recession in the forehead.
I moved to US later, improved my nutrition and regularly used dandruff shampoo. In the next couple of years my dandruff reduced and was eventually gone. However my head still feels little itchy. Sometimes there are acne like or pimple like bumps on my head but not very often and not a lot, just the odd one here and there. Its not like dandruff flakes where the scales are loose. They are stuck to the scalp. When I scratch my scalp at the area of scales, often 5-6 hairs come out attached to a scale/flake. They are not evident in my hair like dandruff, just stuck to my scalp. These are extremely itchy and the temptation of itching is too much. Once I itch it is often better but it doesn't solve the problem. The itching is all over my head more so at the top of the head near the crown and towards the front. I have been consistently losing hair with thinning of hair on the top of the head and forehead.
I do not use any kind of gels, hair sprays, mousses, conditioners etc. I oil my hair every week and wash it off next day. Whenever i touch my head a hair or two fall. Whenever I run my hands through my hair a few easily fall out. I don't feel or have any kind of rashes, patches, itch anywhere else on my body.

On my father's side they had high forehead but healthy dense hair. My mom's dad was however bald and I just hope I did not inherit much from that side. In my recent check up I found that I had elevated cholesterol around 240. I read that cholesterol leads to increased DHT that might contribute. I am following dietary and exercise precautions. I am mostly veg, rarely consume much alcohol and chicken. but also a lot of beef. I read about homeopathy medicines and saw Calcarea Carbonica, vinca minor, phosporous and graphites for quite a few of the symptoms similar to mine.

I know nothing about homeopathy, which is why I want to get an answer from a homeopath or someone experienced who can look at my symptoms and history and prescribe something accordingly.

Please let me know names, dosage and frequency of the medicines I should take.

I apologize if it seems lot of details. I felt that all these details were necessary to explain my condition. I look forward to getting a response here.