Does special Metal Energy reduce damage done to me from attacks by my own Pokemon?
Yes, as long as it is attached to a metal type Pokemon. But keep in mind that Metal Energy does NOT prevent the "placing of damage counters" (not same as "damage done").
Source: PUI Rules Team (2008-09-11)

Relevant cards

Note: All applicable cards may not be listed below.
COL1_87
DP2_120
DP3_130
DP5_95
EX1_94
EX10_97
EX11_107
EX13_95
EX16_88
EX9_88
HGSS3_80
PL2_100
WOTCE1_159
WOTCE2_143
WOTCN1_19