Why does anxiety out of nowhere cause sudden brief dizziness, head rush and slightly faint feeling?

Panic Attack: What u have described is a panic attack, can be treated with medication and therapy.

Panic: Fear or panic leads to release of adrenaline which causes fight-flight response, leading to rapid heart rate, rapid breathing & sweating. Rapid breathing causes drop in carbon dioxide in lungs then blood, which leads to shifts in blood ph (hydrogen ion concentration) leading to dizziness. Another cause is adrenaline leading to narrowing of blood vessels to brain, hence less blood flow to head.