According to the Daily Halacha website:
If a person is unsure whether or not he counted a day of the Omer, and cannot determine conclusively if he had counted or if he had missed that day, he continues counting the Omer each night with a Beracha. This is the explicit ruling of the Shulhan Aruch.
This seems to be the standard ruling for Sepharadim. What about Ashkenazim? The aforementioned website does not cite where this ruling is made, and even if I were to look up the RaM"A there, I have not seen other Poskim anywhere else discuss this (ie., maybe the M"B rules differently from the RaM"A based on some other source, but maybe the Shu"'A HaRav rules in favor of the RaM"A, or maybe RJB"S follows the GR"A, which is different still).
NOTE: This should not be confused with the case of someone who knows that he missed it at night and is unsure if he made up for it during the day. This is about where one is unsure if he counted a day's count at all (eg., it is Day 23 and he cannot remember if he counted Day 22 or not).
As always, CYLOR for practical guidance. I'm just looking for Ashkenazi sources on the matter.