To recover from anxiety, I have tried light/moderate excercise. Is it normal to feel more anxious/show more symptoms like 'lightheadedness' at first?

Absolutely. Exercise often is very helpful for anxiety on multiple levels and the fact that it can cause similar symptoms is actually used as a basis of a type of therapy for anxiety called interoceptive therapy. If you can habituate to symptoms the anxiety loses its power to cause threat or fear.