Unless you no longer want to be promoted, I don't see

why you shouldn't take on more workloads.

If you give up the desire of promotion, you can discuss with her your workloads and make it clear that you overwork and need more resources. Probably they will hire another person to help you. But be careful, the new person will be your peer and also your competitor. 

You weigh pros and cons and make up your mind.

I recommend you to communicate your aspiration to the HR and ask for their inputs. 

Besides, overloaded work volume can not justify promotion. Promotion is not in function of your workload but of the value you can add to the organization. In today's world, unless business is expanding at a very fast pace, companies are conservative and careful about promotion. They either expect you to stand out as to all aspects and demonstrate strong leadership to make changes, or to bring money on the table in no time. 

I fully understand how you feel unappreciated by your supervisor. But think this way, her own position may not be fully secured into the new year. Do you feel better?

Please choose to be happy with your life!

Good luck!