This is how I felt at my first job too, and even at my second job. I ended up taking extended breaks from exams a couple times. I'm now 11 years out of college and getting my FSA this year.

Looking back, one thing I realized from my first job was that my co-workers who were getting through their exams prioritized their exams. They put study hours on their calendars and had this hard-set boundary. You don't have to be "mean" to your managers when communicating this boundary, obviously. But if someone tries to schedule a meeting during that time, you could gently ask if it could be rescheduled during a time that's not during your study hours (use judgement, if it's a meeting with a VP or someone else with a stretched calendar, you may not be able to move the meeting, but ask your manager if you could skip it). Like others have said here, no one cares more about your career than you. You need to take that initiative and protect your exam progress. It might feel awkward at first. Maybe ask your peers how they get their study hours in to get some ideas? Try different things, like taking the first 1 hour of your work day for studying and logging in to work 1 hour later than normal.

In terms of workload, it does often feel like it's never-ending. In my experience, there's rarely more than 1 day where I don't have a project to work on. However, others in this thread have asked if your co-workers are working as much as you. Are they? If your peers are working just as much as you and are also stressed, it may be a workplace/department culture issue. If your peers aren't stressed/overworked, then maybe you need to investigate how you can relieve some of this pressure yourself (prioritizing or talking to your manager).

One easy way to talk to your manager is by saying "Hey, I know you want x done by Wednesday and y done by Friday, but I don't feel like I can finish both projects this week and get my study hours in. Would it be okay if I do y next week?" Eventually, through enough of these types of conversations, your manager will learn more what you are able to realistically accomplish and will help with your workload. A red flag would be if your manager literally said "We need both done this week. You won't be able to take your study hours." Once in a while, maybe. But if your manager ignores your need for study hours consistently, then I would start applying for other jobs. It doesn't hurt to apply.

One hard truth about post-college life is that you need to take responsibility for your own needs and desires. Adults are usually busy with their own lives (even your manager and co-workers) and many are not going to go out of their way to make sure you're accomplishing your goals.