
jucken
to itch
To cause an unpleasant feeling on the skin that creates the urge to scratch.
Der Mückenstich auf meinem Arm juckt unerträglich.
The mosquito bite on my arm itches unbearably.
to itch
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to itch
To cause an unpleasant feeling on the skin that creates the urge to scratch.
Der Mückenstich auf meinem Arm juckt unerträglich.
The mosquito bite on my arm itches unbearably.

to care
Colloquial for 'to interest someone' or 'to matter to someone'. It is almost always used in negative sentences to express indifference.
Es juckt mich überhaupt nicht, was andere über meine neue Frisur denken.
I don't care at all what others think about my new hairstyle.
The grammar reveals the meaning. If a body part is the subject, it means 'to itch'. The fixed negative phrase 'Es juckt mich nicht' always means 'I don't care'.
Mein Rücken juckt schrecklich.
My back itches terribly.
To describe an itch, the body part can be the subject. Alternatively, you can use the impersonal form 'Es juckt mich an/auf...' (It itches me on...).
Mein ganzer Arm juckt.
My whole arm itches.
The colloquial meaning is used in a fixed structure: 'Es juckt + person in the accusative + (nicht)' (It does/doesn't matter to [person]). The subject is always 'es'.
Es juckt ihn nicht, dass er zu spät ist.
He doesn't care that he's late.
The meaning 'to interest' or 'to matter' is very informal and is mainly used in spoken language. It often expresses indifference.
Ganz ehrlich? Deine Meinung juckt mich nicht die Bohne.
Honestly? I couldn't care less about your opinion.
to interest
In negative statements, both interessieren and jucken can express that something is of no interest to someone. interessieren is the neutral standard-language choice. In this meaning, jucken is colloquial, often expresses indifference more directly, and is almost always used in the negative.

Unter Freunden sagt Lea locker: „Die Änderung juckt mich nicht.“
Speaking casually among friends, Lea says, “The change doesn’t bother me.”
Im Gespräch mit der Leitung sagt Lea sachlich: „Die Änderung interessiert mich nicht.“
Speaking matter-of-factly to the management, Lea says, “The change doesn’t interest me.”