Dandruff long term solution. Condition?

I've a combination skin. My scalp tends to change according to the weather. During winters, it's dry after cleaning my scalp with a little flakes, becomes greasy & itchy after a few days(probably 4) if not washed. During summers, it's normal after wash, no visible flakes. After a day dandruff appears. Gets greasy, itchy very fast, due to pollution, comb-ing my hair regularly (with a curly comb which is smooth, I've wavy hair that starts after 3/4 inches from above). Itching is extremely bad, I used to wash my hair everyday years before. However, I've not been doing that since 2020 staying at home. I don't use oil, it gets greasy and itchy. I use it extremely-rarely, probably an hour before wash.  Problem : 1) Dandruff. Tried scalp pro, gives cooling but effective only for a day. Looking for long term serious solution. 2) Extreme Itchiness after second day for wash. I don't have lice only dandruff issues. 3) Is there any lotion+shampoo that would help with my condition?