I suspect you will get better quality product and more choices from a natural store. In my experience drugstores tend to have a limited selection of organic products. Online can be a pretty good way to purchase stuff too.
Acure Organics has a good line up of natural face cleansers, shampoos, body washes, etc. Not too expensive either. Take a look at their website. You can get sample sizes for some of their products by calling their customer service group.
I have been through a very similar situation as what you describe. First derm was insistent on antibacterial treatments. Kept trying them for about a year with no improvement / worsening of condition. Went to a second derm for a second opinion. Second derm did some small biopsies which confirmed the issue was fungal. Ketoconazole shampoo and oral antifungal med have pretty much cleared up my problem. You should get a second opinion from another derm. You need to know (with certainty) what is the nature of your issue so proper treatment can be prescribed. Visual assessment may not be adequate. Good luck.
It took that long because the first derm only did a visual assessment and prescribed antibacterial treatments (doxycline, clindamycin, etc) when in reality my problem was fungal. My condition actually worsened because bacteria was wiped out, allowing fungas to thrive (the two compete for real estate on your body). After 1.5 years of this I went to a different derm for a second opinion. He did a biopsy and determined my issue was fungal. From that point it took about a year to get me cleared up. Sometimes I still have minor flare ups that occur, particularly in hot weather.
I don't feel qualified to answer the question about taking doxycyline and terbinafine at the same time. You need to do a bit of investigation on that one....
The biopsy is a wise move. That is the best way to determine if the issue is fungal or bacterial. You must know that to select the proper treatment. Using antibacterial meds on a fungal issue may very well cause the condition to worsen. I have personally been through this situation and it took 2-3 years to get it sorted out and cleared up.
The Nizoral shampoo available OTC has only 1% ketoconazole. There is a prescription version of the shampoo that is 2% strength. It also has less junk in it like fragrances, surfactants, etc. I wash my scalp, face, torso with it every other day. I am prone to that folliculitis condition and it has been somewhat of a miracle product for me.
I also have skin troubles that flare up when i get over heated and sweat. My derm has done a few small biopsies and diagnosed me as having two conditions: 1) Grovers disease, 2) Pityrosporum folliculitis. Try looking these up and see if they match what you are experiencing. Sweat and heat are triggers for both. The first condition is believed to be due to occluded sweat glands. It is almost like the sweat glands are partially blocked, the sweat collects in/under the skin, inflammation and small infections result. Hope this helps.