Both the Idioms draw on & draw from are correct and almost same meaning but are used in different contexts.

a person or organization need some inspiration, as a person or organization need to get any idea or any advice from someone. e.g., Ankara (Japali), a person or organization need to get advice. How can I start this project as a hobby? I am more than just an eyesore. If you can draw on me to your advantage, let me know. By the end of the contest I had drawn upon all the energy I had.

In this draw on tends to be more asking attitude the user is not very sure and is in a state of inconvesion. He / She might be asking for some help.

same as draw from, to get inspiration from someone. e.g., if you draw on or draw from something rather than draw from someone. She draws inspiration from her parents and the creative mind of her students. She makes huge ideas from her Father.

Here the draw from sound that the user has already decided what he/she is going to do and is talking about her experience. Lets say I draw my groceries from Walmart?