Bismihi ta'ala

Yes, it is permissible to sketch an image depicting certain events of Karbala, through the eyes of an artist. An example for this is the creative art of Mahmoud Farshchian. If done in a right way, it would be a wonderful method in conveying many positive messages, and hence it would be a recommended and encouraged act. 

However, in regards to the Ma'sumeen, or members of Ahlul Bayt (a.s.), one must be very careful in how they are drawn. To draw any of the members of Ahlul Bayt (a.s.) in itself is not specifically haram, unless it is drawn in such a way that is insulting or lowering of their status.

We do not have any authentic narrations regarding exactly how they looked, so an artist will not be able to rely on anything that can be used as a basis. 

It all comes down the the imagination of the artist, and how they visualise how someone would look at that time, which cannot in any way be verified. This is why some of our scholars, although do not prohibit it, they do say it is not free of problems and should be avoided. 

Sadly, some images are drawn in an innapropriate way, being similar to images depicted in Churches, or images drawn of Jesus (a.s.), or drawing the Ma'soom like as if they have makeup, or thin eyebrows, or other common criticisms usually directed at these commercial pictures that we can see in the some places. 

An artist is able to convey many artistic and spiritual messages beyond the facial depiction, and we must always remember that it is our duty to look beyond the physical material element of our relationship with how we can connect with them (a.s.). 

With prayers for your success.