When I I fell asleept i on the train the other day because I was very tired, and I felt something touching my face.

I fell asleep

I woke up with wondering and realized that a baby sitting next me touched my cheek.

When I slept iile I was sleeping on the train the other day because I was very tired, I felt something ion my face.

{I woke up with wondering what had touched me | I startled awake} and realized that a baby sitting next meto me had touched my cheek.

My exhaustion was blown awayevaporated!

W The other day, when I slept in the train the other day because I was very tired, I felt something in my face.

Sleeping because your are tired sounds repetitive. It could be assumed that your are sleeping because you are tired so delete

I woke up with wonderingconfused and realized that athe baby sitting next me, touched my cheek.!

Is "wondering" a person? A noun? Or are you trying to say an emotion?

My exhaustionI was blown away!

or "I was shocked", "I was so surprised", "I was dumbfounded"

WThe other day, when I slept ion the train the other day because I was very tired,. I felt something ion my face.

I woke up with wondering and realized that a baby was sitting next me. The baby touched my cheek.

My exhaustion was blown away!

Not sure what you mean by 'exhaustion' in this case. Maybe you are trying to say 'My expectation was blown away!'