You HAVE to establish a left handed average. Also,once your shoulder DOES heal,if it is still this year, then before you bowl every week you must tell the opposing team captain which arm you are going to use in order to use the correct average for handicap determination.
This rule was established in order to prevent sandbagging----and I am NOT accusing you of this. I have seen that happen in the 80's so that 200 plus bowlers could build up handicap before tournaments.
Good luck and I hope your shoulder heals........
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Chris