I hope all is well! These are two great questions, and they are ones that I found myself asking when I was a freshman in college. While I was a History major and not an Art History major, I believe the answer is the same.
When I was younger I always enjoyed history in school and that loved never left me as I got older. When the time came for me to declare a major in college, I made the decision to pursue a degree in history, despite urging from my father and others to pursue a degree in business. I had the ability to take a few business courses during my freshman year and I actually did pretty well in them, but they never gave me the mental stimulation and pleasure that my history courses did. So, I figured that if I was going to be spending enough money to buy a house, I had better really enjoy what I was studying, and made the decision to pursue a Bachelors Degree in History.
Historically, there was this notion that History majors would either become a lawyer or a teacher, and while many history majors do in fact become lawyers and teachers, the career possibilities are endless. This is in great part because when you study history, you'll be incredibly well read and you'll most likely be able to write better than most of your peers. Not to mention, you'll be able to hold interesting conversations with future employers and co-workers. I currently work for one of the largest technology companies in the world, and the majority of people I work with have an educational background in the liberal arts. None of us are tech geniuses, but we can all communicate clearly and effectively with our customers because of our backgrounds. Of course we have to know what we're talking about when it comes to the technology, but none of us could develop an App or code.
Ultimately, "worth" is going to be different for everyone, but I can assure you that you won't be putting yourself at a disadvantage by studying Art History. If you wanted to pursue a career in medicine or engineering, I would advise studying something else, but besides these few exceptions, there's nothing you can't do. And if you decide you want to be a doctor, you can always go back to school! At the end of the day, if you follow your heart and work hard, there's nothing you can't achieve in this world. Was studying history worth it for me? Absolutely!
I hope this helps. Please let me know if there's anything else I can help answer for you. My thoughts and prayers are with you and your country, and I hope all of your loved ones are alright.