Do you have bedbugs if you get bitten on your sofa and mattress and the bites go away relatively quickly?

It is difficult to say from information you give. People do not "have" bedbugs beds do,

But "bed" means somewhere people sleep, which includes all kinds of bed structures including sofas or any other dossing down area in any place. It is therefore quite possible if you see little red marks on your skin and it itches after you wake up from sleeping anywhere it could well be bedbugs. But it could equally well be another sort of insect, such as mosquitoes or fleas, that is feeding off your blood.

Fleas are most likely if you have pets in your home, such as cat or dog, and fleas normally like people who are dirty to feed on, whereas bedbugs seem to feed on even the most spotlessly clean people and do not associate with pets. Mosquitoes are not particular but need water, such as rain to exist which neither bedbugs nor fleas do.

If during the day when tidying up your living room or making the bed you do see brown flat looking insects running around very fast when you disturb them trying to get out of the light, then you could well have bedbugs in your home.

Be aware the bedbug biting you is only on your body for about 5 to 10 minutes at most usually much less, and most usually they will only feed off people who are asleep and when it is dark, whereas fleas may stay on your body and go under your skin as they live on a host not hide in the bed or near it like bedbugs do.

Bedbugs only come out of their hiding place to have their meal for about these 5 minutes, then they return to their hiding place usually long before you wake up.

So they may be difficult to spot, and during the 5 minutes or so each bedbug is actually on your skin sucking your blood you do not normally feel anything, because it injects an anaesthetic into you before piercing your skin to insert the tiny tube through which it sips your blood. You will only start to itch where it has been when the anaesthetic it injected into you has worn off, then with some people the itch can be absolutely maddening, but others hardly notice anything.

Marks on your skin also vary a lot in appearance from person to person after bedbug bites. Another clue that there may be bedbugs in your home is if you see little red marks of blood on your bedding, particularly on sheets or pillow case or on the sofa or on the walls near where people sleep.