I do all injections right after getting out of shower. Have done this for over 5 years. Never used alcohol or peroxide in those 5 years either before or after injections..
I dont use bandaids unless I cut myself shaving..

I always nick myself on the elbow or forearms..
Only thing you can catch from the gym that I know of is hepatitis. As for catching an abcess, hardly. Its from injecting bad gear like you said, and not from some unsanitary gym equipment. Being in my line of work, you are constantly washing your hands, so it is normal for me after I work out to wash my hands.