Kate:
Acne can cause pimples and pustules on the face, chest, and back, but pimples under the arms or in the pubic hair are different. While you may have acne as well, it sounds as though the more widespread skin inlammation (and perhaps all of it) may indeed be related to secondary bacterial infection to which eczematous skin is somewhat more prone. The bacteria involved in this is more oikely than not to be staphylococcus ("staph.") If so, an antibiotic other than a tetracycline would be more appropriate. Also, the underlying eczema may need some more aggressive tretament, topical or orla, than you are now using.
I would broach these suggestions with your physician, or with a consultant if you can arrange to see one.
I believe you can attain substantial relief in relatively short order.
Good Luck.
Dr. R