I hide a card and then force a showdown the same turn on the same battlefield, can I review the hidden card?

Yes, you can review your own hidden card at any time.

According to Rule 128.4, a card that is facedown at a battlefield is considered Private information. This means that you, as the controller of that card, may read or look at its face at any time, regardless of whether a showdown is happening or what turn it is.

While you are allowed to check your own hidden card, please note the following restrictions regarding its use:

• Timing: You cannot play a hidden card on the same turn you hide it. You must wait until at least the next turn to play it (see FAQ #3046).
• Privacy: While you can check your own hidden cards, they remain private information to your opponent. You do not reveal them to your opponent until you actually play them or if they are forced to change zones (Rule 421.4).