If your not sure about the power capability of the NANO's 3.3v supply, there is a TX0108 module available that has built-in adjustable LDO regulator which can supply more current at 3.3v. The module is made by BLKBOXme, part number BB-0108B. I sourced one from eBay.
The module's regulator IC is adjustable by a small pot, but also pin compatible (SOT23-5) with fixed 3.3v LDO regulator. I used this module but substituted a Texas Instruments TLV70033DDCR regulator for fixed 3.3v to supply a 2.42" OLED. Small form factor of SOT23-5 makes the substitution more difficult.
Per the product page, Uno's 3.3v is only good for 50mA. Nano's product page doesn't specify.