Wouldn't that effect the 10A reading too?
I think there is a good chance your meter is working just fine.
On the milliamps setting, it has a resistance (shunt) of about 2 ohms. So 1.5V and 10+2=12 Ohms, can be about 120 milliamps.
The 10 Amp range has a very low resistance (shunt), so will give a current much closer to the 150mA.
Other meters can have different resistances (shunts), so can't necessarily be used as a comparison.
Really you should be using a constant (and ideally calibrated or known/accurate) current source to check it properly. This "rough" way with the battery is just confusing. The battery has an internal resistance as well, which varies.