networking question: 2-way messaging w/o wireless modem config?

[haiticare2011 at gmail.com]

I have a Raspberry Pi board with a wireless usb modem on it.
I wish to be able to message 2-way with the board from 
across the internet, without having to open ports on the wireless modem. Is there
 a way to do this? I have been looking at udp, but imagine that a udp packet is 
allowed in, but not out?
The amount of data transmission I want is very small, maybe lt 30 bytes. 
So a client http request could include this data?
I have been looking at messaging systems like MQTT as well, but don't know if they require opening a port in the typical modem-router.

Any ideas appreciated!