Can you get an over-the-counter corticosteroid cream (i.e. Benadryl/diphenhydramine) where you are?
I only ask because, for what it's worth - I have insanely sensitive skin and I have major skin reactions to many things. My mosquito bites look so bad that a doctor I showed one too truly wondered if it was mosquito (it was), or if I had been bitten by a brown recluse spider and was having necrotizing flesh breakdown. The itching from a <1cm bite inflames and causes severe itching in an area surrounding it on the size of a grapefruit or larger. Nothing touches the itching except burning/scalding the surrounding flesh.
Anyways - I've recently started on HRT myself, and do have an itchy reaction to the patches. I decided (without much hope, as it does nothing for my bites) to try some of my anti-itch cream on it - and to my surprise, it actually works quite well. So I was wondering if you'd tried anything like that.