Thank you for the additional information.
The usual first-line treatment for oak mite bites are treatments that are really oriented towards the reaction to the mites. From that perspective, the primary treatments are steroid creams to control the inflammation and antihistamines to counteract the reaction. You have tried the strongest over the counter steroid cream with the cortisone 10 and one of the common antihistamines. Bag balm is soothing, but has no direct action against the reaction. The next steps are either a stronger steroid cream or systemic steroids, but this would require a prescription. There are several other antihistamines available over the counter, such as Claritiin and Zyrtec. It is not that the other antihistamines are stronger than the Benadryl, but that they are in different chemical classes and different antihistamines work better for different people. One of the other advantages of Claritin and Zyrtec is that they are not as sedating as the Benadryl, so may be a better option for someone who drives a semi. There are also other topical treatment that may be soothing, such as calamine lotion. It also may be soothing to soak in warm salt water.
In your case, if it is not possible to get into a doctor, then using a different antihistamine while continuing the cortisone 10 and soothing interventions would be reasonable.
Some of the oak mite bites can develop an infection on top of the original bite, and if this happens, it would require antibiotics.
Since oak mites generally do not like humans, we usually do not have to treat the mite directly on the body. Interventions to clear the home environment may be necessary, usually involving cleaning with soap and hot water. However, when there is a mite infection that requires direct treatment, permethrins is a common first-line treatment, which is likely the active ingredient in the product recommended by the Pharmacist. Parthenon is a company that makes several different creams.
If I can provide any further information, please let me know.