It might be too early to tell for you just yet, but the progestin in your combined patch might be not the right fit for you. However, I can say that I get fatigue from every progestin at the start (I tried a few different ones, as I am intolerant of progesterone) and for me that seems a passing side effect. I would recommend to try for a few months (if this is the only bad side effect) to see if this gets better, but know that there are lots of options to try when it comes to hrt.
(I started on dienogest as my progestin 8 days ago and I’m having the same side effect. It’s bad, maybe worse than I had before, but other side effects have been small, which is a big plus for me with my intolerance).
Itchy scalp:
I get an itchy scalp if I use hair products with the itchy M’s in them (preservatives that some people have problems with, but aren’t bad ingredients, so they are used pretty often). Also, I can get itching from a lot of scents, but not all, so for me this is trial and error. With these ingredients, for me it is mostly a problem with products that stay in your hair, like leave ins, creams, gels (I have wavy-curly hair, so use these). If I’m really sensitive to ingredients, I also get itching from shampoo and conditioner. (I give everything that causes itching to a friend that also has curly hair, but doesn’t have a sensitive scalp. She is really happy about my sensitive scalp

)
Often, if itching starts in perimenopause (or when hair is curly) it is caused by dry scalp, so using more moisturizing hair care products can help if that is the case. After I’ve worked out, if I’m not washing my hair, it helps to use a serum of refresh spray on my scalp (boucleme has a really nice scalp refresh spray).
As I Am (brand) has a dry and itchy line, that some people find really helpful (I’m not crazy about them, but if you also have dandruff it’s worth a try, because there is an active ingredient in there to treat it).
So, just some options to try, reasons for itchy scalps are many, so solutions too.