A tick bite can cause immediate, intense itching in some people due to the toxins and irritants in tick saliva. However, itching doesn't always occur. For this reason, if you spend time in a tick-infested area, it's important to check your whole body for ticks after you leave.
If a tick bite leads to Lyme disease, it can also lead to the development of lesions on the skin known as erythema migrans (EM). These often don't trigger any further symptoms, but some people report that they feel itchiness and burning around the area of the lesion.