How to spec out a relay correctly
Yes, you should use a relay with an inductive rating. Somewhat excessive carry current often isn't an issue (depending on the design of the relay), the limitation is the contact life span. Excessive carry current causes internal heating. Switching excessive current causes excessive arcing and reduces the life of the contacts, or can cause welding of the contacts. 

One approach is to use a relay with a heavy compressor rating and hope for the best. Something like Omron's G7L series. These will probably be much more expensive, larger and draw more current than your 3A relay, but the life should be much more impressive.