One word that might be a good fit is the verb hound (and its synonym nag might work as well.) Neither word necessarily implies loud shouting the way yell does.
Here is one definition that I think pertains to your context:
hound (trans. v.) to urge insistently; to nag: hounded me until I agreed to cut my hair.
So, if my son was not performing well in school, I might say:
I will hound you until you take school more seriously. These grades need to get better.
But there is yet another definition which happens to match your picture quite well:
hound (trans. v.) to pursue relentlessly and tenaciously
Those defintions came from Wordnik; M-W has similar definitions:
1 : to pursue, as if with hounds (i.e., with hunting dogs)
2 : to drive or affect by persistent harassing : They hounded me with questions.
Although the word hound is often used negatively, it can be used in a positive sense, too, when someone is being urged do something positive with their life. For example, on a teacher review site1, one former student wrote:
Do whatever you have to do to get Ms. A. She wouldn't let me fail like all my other teachers have in the past. She hounded me about my grades and my "intellect". Now I'm going into my junior year with a high GPA and the prospect of attending a 4 year college.