For me I have had itchy skin since I was diagnosed and it continues till today. The one thing that almost but not quite controls it is a high dose of an oral antihistamine tablet. Although you can buy these hay fever tablets over the counter I wouldn’t recommend people just buy them but instead talk to their doctors first. The one I take for example can in some people cause changes in the ECG so we checked that hadn’t happened to me (which it hadn’t!)
I’ve found over the years that I’ve had itchy skin that I’ve had to change which one I’m using to try and get better control and to increase the dose above the normal licensed dose. A GP may well be willing to discuss with you which one makes sense for you to try, or you could be asked to see a dermatologist.
I should say that if you have any sort of rash it is vital to make sure you find out what the rash actually is rather than just treat it. And you should do that quickly. And I would definitely argue that a brand new itchy or painful rash in a patient who had blood cancer should be considered a medical emergency until its proven not to be.
It could be shingles (usually but not always this rash is in a band on one side of the body) or some other infectious cause (even sometimes a bacterial skin or hair follicle infection), or there are some other important causes (sometimes for example if you have recently started a medication you might have a skin reaction to it).
So with an abundance of caution and ready in most cases to be told it’s nothing to be worried about if a new rash appeared I would definitely book a same day GP appt, maybe ask a pharmacist, or go into an Urgent Care or even an A and E. If it is shingles (which doesn’t always hurt at first) or some other infection you definitely need rapid treatment and hours sometimes count.
I do find “I have a blood cancer and so am immune compromised and I’m worried this symptom might mean I have an infection” is the best way to introduce yourself to new medical stuff in such a situation. They should certainly then understand why you are there, will hopefully prioritise you, and will be only too happy to reassure you and send you on your way if the rash isn’t anything to be concerned about.