ZHU Developmental Controller described a loss of separation event during multiple weather avoidance maneuvers near multiple sector boundaries.

Narrative

A Collision Alert went off between Air Carrier X level at FL350; deviating for BTR around an extended cell of weather from the Houston terminal area to northeast of SWB. The other aircraft involved was deviating for SPS around the same weather cell. We were receiving reroutes from ZME and ZFW that were flying along the multiple Boundary/Sector lines that the three centers share. It appeared that a lot of the Houston Terminal departures were turned early adding to the complexity of the situation. The addition of the re-routed aircraft; along with the MSY arrival; made the traffic search more complex. Evasive actions were taken to help achieve separation once the alert was noticed. Add more training tools to help learn about weather and dealing with the effects of deviations. Most training deals with learning separation. Weather is a dynamic situation that could be taught with periodic and effective training. Keeping aircraft on filed routes when there are TMU reroutes in effect; also; utilizing other routes to better help with deviations when there is a line of thunderstorms that have already developed.