Electronic – Noob Building a Terminator

cameracircuit-designled

So I'm building a life-sized battle damaged terminator with a 3.7v 240 mA spy cam in the human eye, and a red 1.8V LED in the exoskeleton exposed eye. When the camera is powered by a 3.7V 340 mA power supply, I want the LED to also be powered but want to make sure I don't overheat or under-power anything. I'm guessing at a parallel(?) circuit like the below:enter image description here

Am I on the right path here or do I also need to up the power supply to account for the 1.8V LED? I understand I only need a 95 ohm resistor but all I have are 100, 220, 330+.

Update: So I found the actual LED Datasheet:
enter image description here

Does this mean the LED is actually 2 Vf and 20 mA?

This is my first project and only have worked on basic automotive electronics so my apologies for my ignorance in advance and thank you for taking the time!

UPDATE:

So, turns out the "3.7V" power supplies were actually reading 8V+, so I swapped them out for a standard 5V .5A USB Charging brick, which worked on the camera alone before. Trouble is, with the LED, the Camera would not work, so I tried a 5V 1.0A charger, same problem. So I tried a 5V 2.1A charger and it worked! Trouble is, now the camera overheats. (registering over 40C). So with the revised diagram below, can anyone tell me how I should be able to safely power the camera and LED without overheating the camera while using a basic USB charger?
enter image description here

Best Answer

All you need to worry about is supplying the correct votlage with a supply that can produce enough current.

A 100 Ω resistor is plenty close enough.

This should work fine.

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