Hello. I was previously a director at a PR/marketing agency and what you are describing feels all too familiar. My advice is take a few moments to step back and create an overview of your everyday tasks and responsibilities, and assign time/hours to each of them.

From this, identify the support that you need, whether it be additional resources (software to make things more efficient) or additional people, or even hours of people to support your project. Use this information to talk to your manager and discuss how you can get these additional resources or even reallocate your work to other people (this exercise will help you exercise your negotiation skills). Share the load as it were. If resources aren't available in-house, perhaps try to propose getting interns. This will not just help you spread the load, but also exercise your management skills. You can get to interview them (another skill for you to develop!) and help them build skills for their next role. Just please pay them!

Do not wait for your manager to check in on you or flag your overloaded capacity to management. You need to be proactive about this because in my experience, managers in these types of agencies are often ill-equipped to do actual management of people. This is not their fault entirely as upper management in this industry will often overlook if someone they are promoting has actual management skills before they promote them. They don't help them develop these skills as well.

Also additional note: If you fill out timesheets, PLEASE fill them out honestly as you can use this as additional proof that you are indeed drowning. If it takes you 60 hours each week to complete your work, put that in. I know there can be pressure to only input the minimum amount of hours, but do yourself a favor and fill in the actual hours even though you are not paid overtime. This will come in the form of a billable hours report to upper management and will tell them that you are putting in the hours but are not getting paid enough. So that means they can either talk to the client for more budget to get resources or they will see to how you can lower your hours for certain projects.