Is there a way to see who voted (upvotes and/or downvotes) on your answers and/or questions?
No, voting is by design anonymous. Not even ♦ moderators have access to information on individual votes.
The only way you will find out who voted for you is if someone decides to leave a comment saying so and maybe their reason. This doesn't mean they couldn't be lying also.
(To tell if, and how, you voted on a specific post, your votes are stored in a database. And of course Stack Exchange employees do have access to that information, but it's only used in exceptional circumstances, such as investigating voting fraud.)
By design, the site has anonymous voting. Except for developers, NO ONE has access to viewing such things, not even moderators. Having voting made public would cause nothing but problems
Users may bug others about down votes they gave out
Who needs to know up votes? You just got +10, what more could you ask for?