This rule has changed over time. There was a time when the player could elect to play left handed (if he were right handed) and upon deciding his swing was impeded, and a drop was allowed, he could take a drop and then switch back to his normal right handed swing. At our state amateur I had this come up one year and was advised that the rule for relief was only available if it was your normal swing that was impeded, however, I was free to swing away left-handed, just with no relief. You always can swing from either side, of course, but you can only take relief from your normal swing impairment. I started golf playing left-handed and then switched to right handed so when near a fence or a tree, I will often swing left-handed either by hitting the back side of a low iron or by flipping a lofted club upside down.
I think a long time ago it may have been illegal to hit a ball with the back of club rather than the face, but that was so long ago that I forgot if that was true or an old wives tale. The rule book then was pretty small and you could carry it in your back pocket. Now my "Decisions on the Rules of Golf" is a pretty big book, and I have given up trying to remember all the rules. There have been a lot of changes in over 60 years of playing this game, and I no longer claim to know them all. Also, there were slight differences in PGA rules and USGA rules, a trend that is tending to be more limited now.