Well your program is way optimistic. Too many cities and travels in 3 weeks.

Delhi/Jaipur/Jodhpur/Jaisalmer is one direction. (Drive from Jod to jaisalmer is amazing)
Amritsar way up north.
Varanasi way east.
You will not be able to do that. And if you do. You will have just enjoyed transportation... and not photography.
You need to focus on one region and stay. I know it's frustrating but...

Holi is one of the most fantastic time to enjoy. But very stressful with a camera.
All that paint flying around is impossible to avoid to say the least. And you are a target of choice.

Agra is a touristic nightmare.

If I was you I would focus on Rajasthan only.
If it was me I would go to Varanasi and stay there. 3 weeks is not even enough. But it will be worth it.
:-)

Ex India addict with 10 years of intensive use.
G.