After getting my second itching tick bite in a week, I thought I'd try the remedy used for mosquito bites. I heated a tablespoon in tap water. Then I held the back of it against the tick bite until it cooled off. The itching immediately went from 8 on the tick itch scale down to 1. I thought the effect might eventually wear off, but when I woke up this morning, it still felt almost nothing. Therefore I consider the experiment successful.
In the case of mosquitos, it is a protein that causes the itching. Heat destroys the protein and makes the itch go away. I guess it may be some similar effect in tick bites.
Write in the comments if you try this.
(Photo from the public domain)