I recharacterized my Roth IRA contribution to a Traditional IRA contribution last year. Can I have it reversed?

No. Once a recharacterization is processed (completed), it becomes irrevocable. You now have a traditional IRA contribution. However, if you are still within the deadline for completing a recharacterization, you may recharacterize that traditional IRA contribution to your Roth IRA. For more on recharacterizations, please see the definition here