Current limit on Nano, 5 shift registers

Hello all!
I loved the idea of Arduino the day I found out about it. After getting a starter kit I got myself to learn how to use it. Made several small things but never actually wanted to keep them. That was until I got inspired by a Fibonacci clock https://goo.gl/images/BhLVEJ
I am making my own version of it, a bit different, the golden ratio spiral will be there, too. Using DS3231, 5 shift registers and 37 LED diodes. Currently switching from breadboard prototype using Arduino Uno to a PCB with Nano.
My question is about the current used by this setup. Found out Nano has an absolute limit of 200ma. When time displayed is something like 11:57 almost all LED are meant to light up.
How to calculate if I am within limits?
Does changing resistors will change it? Currently using 220 Ohm and 330 Ohm on the breadboard.
Should I connect power pins of my five SN74HC595N registers to Nano’s VIN insted of 3.3v? I am thinking about using a single 18650 cell (4.2 down to 3.2 v). Do I need a voltage regulator for it? I am really afraid to give the PCB version a test.

All replies highly appreciated!

How to calculate if I am within limits?

Add up all the current you are expecting the Arduino to source or sink. The sum has to be less than the limit.

Does changing resistors will change it?

Yes it will change the current taken by the LED and so change the sum total of current.

Should I connect power pins of my five SN74HC595N registers to Nano's VIN insted of 3.3v?

The power pins should have the same voltage as the signal voltage, which is the power given to the Nano's chip. Also each shift register should have a 0.1uF ceramic capacitor between the power and ground pins.

Consider using a tpic6b595 instead of a 74hc595 if you are worried about current limits.