This is a great question. While there are many topical medications (both natural and pharmaceutical), success with either can be limited.
I understand your frustration. A simple topical that I will have my patients use is a colloidal silver gel. Silver has remarkable healing properties, a fact that has been known from centuries. Before antibiotics came into favor, silver was a favorite among doctors for the treatment of diseases, infections and skin problems. It works very well on all types of pathogens including bacteria, viruses, fungi, yeast, egg-stage of parasites and multi-cell organisms as well. It has some benefits over antibiotics by which it is difficult for an organism to become resistant to it because of the manner in which it works.
While you can use colloidal silver in a spray form, I like the gel as it seems to stay on the skin more effectively. However, many of my patients have used the spray with great results. Regardless of the form you choose, the concentration is important. 10-15 ppm (parts per million) is my recommendation. Also, the finer the concentration, the easier the silver can penetrate through the skin. I usually use gel and liquid from a company called ASAP. It works quite nicely on people of all ages and is pH balanced. Besides treating acne, colloidal silver is very useful for other skin conditions like burns, cuts, conjunctivitis, dermatitis, eczema, hemorrhoids, insect bites, rashes, razor nicks, sunburn, warts, wounds etc. From this perspective, it should be staple in all first aid kits.
As you will hear me say time and again; treat the cause!
Acne is a symptom of a more systemic imbalance (contrary to the belief that is caused by bacteria). While acne is related to dysbiosis (bacterial imbalances), it is not the cause, and so therefore, I always seek to determine what types of imbalances exist that are perpetuating the condition. For acne, I always, start with testing for food allergies, hormonal imbalances, and ensuring proper (daily) bowel elimination. These factors identify the cause over 90% of my patients with acne. So yes, treat the surface (skin), but always remember, the skin may be just the tip of the iceberg.