Is one obligated to have ones garments checked for Shatnez in todays world? Could you please send source of the answer?

When it is easy and inexpensive to do so, one should check woollen garments for shatnez even when use of linen is infrequent. In garments where the use of shatnez is not infrequent, the inspection is mandatory even when this is more difficult (see Shu”t Iggrot Moshe Yoreh Deah I 72).