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Is it possible the water line may have some small amounts of ice causing the water to drizzle.
No, not unless the outside temperature is below freezing and the pipes have frozen again.
More likely that some debris from the rupture and the repair is trapped in the aerator and blocking the flow. Remove the aerator and see what flow you have.
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I insulated really good
Unless you live in an area where the temperature drops below freezing only for a short period of time, insulation alone will not prevent freezing. Insulation only slows down the heat loss, it does not stop heat loss. You must provide some source of heat, such as heat tapes, if you want to prevent freezing.
