tl;dr: start simple with simple programs that will be part of the final device
Your device will need an Arduino, some means of receiving messages, a way to vibrate and… some source of power for all that.
Your device will need some slightly less than trivial programming.
If your group are all beginners in the areas of expertise that might be required, the project of a portable bracelet is ambitious but not impossible.
I suggest you start with a non-remote controlled non-portable not wearable not battery powered version. As simple as something that will light an LED for 5 seconds when you press a button.
No time you take getting that to work will be wasted.
For getting the signal from the world there are a few choices. Some Arduino boards have build in Bluetooth, or can have a Bluetooth module attached. This would be the least you'd need to "hear" from a cellular telephone.
In parallel with getting the communication to work you can think about battery power. Some Arduino boards are already equipped to accept the power of one cell; some can charge such an attached cell, but that is not important.
The vibration can come from a vibrating motor like those found in phones. That will require a bit of circuitry as Arduino boards can certain control such a motor, but not provide the power it might take.
Still not portable, still not battery powered. But a long way down the path.
Sry no specific hardware recommendations - all I can think of will end up being a bit clunky, maybe a real fashion statement. 
And I make no sense of this
send the message to the Arduino to vibrate and then maybe just taping it on to a clock or something?
Is this clock with the Arduino taped to it on my wrist or what?
HTH
a7