The most common insect that readily makes it's our casa it's casa is the flea. Fleas find an ideal environment in our rugs. They can also go without food for many days. They can lay thousand of eggs in their life-cycle. Whats amazing is that the eggs, once deposited in the naps of a carpet will remain un-hatched until it senses vibration (from humans walking) signaling that dinner has arrived.
To verify that there is an infestation place a white bed sheet on the ground outside. Holding a section of the rug over it shake vigorously for a few seconds. You should now have a clear look at everything that resided in the carpet.
If you are certain the marks are not a skin re-action to a substance on the rug, but was caused by a blood-sucking insect, have a professional insect eradicator access the situation and prescribe a treatment. They are best at knowing what and how to remove the pest that may be residing in your home.