Anonymous I HAD TO REPAIR MY CAR YESTERDAY . OTHERWISE, I COULD NOT GO TO HER BIRTHDAY PARTY OR I MUST HAVE REPAIRED MY CAR YESTERDAY. " There are other tenses you can use for the "otherwise" clause, which many members will prefer.
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AnonymousI HAD TO REPAIR MY CAR YESTERDAY . OTHERWISE, I COULD NOT GO TO HER BIRTHDAY PARTY
OR
I MUST HAVE REPAIRED MY CAR YESTERDAY. OTHERWISE, I COULD NOT GO TO HER BIRTHDAY PARTYI believe you want your first example, with "had to."
There are other tenses you can use for the "otherwise" clause, which many members will prefer.
Eg, "Otherwise, I could not