I cannot stress how important it is not to pick your skin, its probably one of the major causes of your acne. When I reduced my skin picking my skin improved quickly. I know what its like to constantly pick and not notice, you should look into the skin picking forum of this site, in addition you should visit stoppickingonme.com which tells you in lots of detail the damage you're doing to your skin when you pick. But you will NEVER be clear if you don't break this habit trust me!
If you have under the skin pimples along your jawline, sounds like your acne is hormonal and I would suggest the pill, but make sure you look into the side effects. But prioritise the skin picking and i think you'll find the redness will really go down!
I also suggest don't expose your skin to UV as skin weaker to such radiation when on minocycline