Greetings..
I assume no rash but only itching over both hands and legs..
There are few possibilities..
It could be because of antibiotics you have used for typhoid or it could be dryness..
Use a good moisturiser like either venusia or sarna lotion morning and night and tablet which contains montelukast like tab dazit-M morning and night for five days
Visit any nearby dermatologist if rash appears
Next Steps
if the symptoms doesn't reduce within 5 days, get blood tests done
thyroid function test and random blood
sugar to rule out if this is the primary cause.