You can put clear finger nail polish over the pins you are afraid of touching. The higher quality polish, the longer it will last. If you ever need to rework it then the soldering iron will burn through the polish and create extra smoke. Conformal coating is what the industry uses to protect boards from chemicals and moisture, but is more expensive and harder to rework.
Flux comes in many varieties. Rosin or No-clean are most likely what you have. Rosin should be cleaned off with rubbing alcohol and a toothbrush if you want the board to last decades. No-clean can stay on the board, but can also be cleaned off in the same manner. If you have water-soluble flux then you must clean the board thoroughly with water to prevent future damage from the aggressive flux.