So I purchased a min 3V relay switch (https://www.digikey.com/products/en?keywords=ADW1103HLW) and am trying to turn it on with a simple transistor setup. The data sheet says I only need about 66.7mA (operating at 3V, even less for 5V) for the switch to turn, and my ammeter is currently (no pun intended xD) reading 90mA through the switch. So the circuit seems to be working correctly, yet the switch still will not throw. Ive tried two different switches to rule out the switch being bad. Can you guys recommend another approach to figure out whats going on? Thanks!
That is a latching relay - you apply a short pulse of power to the coil with one polarity to close the contact, and pulse with the opposite polarity to open the contact. This is a relatively rare type of relay, and will not work with the circuit you show.
A "normal" (non-latching) relay will move the contact when power is applied and held, and release the contact when the power is removed.