I have what I guess can be described as a mild case of bed bugs in one of my cars, weird I know but in the process of taking care of it. Anyway I get bites around my elbows and it gets really itchy and bothersome for almost a week. What I found works wonders for me is simply taking 1000 mg of motrin once a day. I had a huge welt that looked swollen and red and taking motrin calmed it down and made it stop itching for almost a full day at a time.
Unlike those of other insects, bed bug bites may sometimes appear in tight lines of multiple, small, red marks where multiple bed bugs have fed along an exposed area. Bed bug bites can cause itchiness. Initially, a victim may detect a slight burning sensation. The burning area then develops red bumps, known as papules or wheals (rash). In extreme cases, bites may swell dramatically or turn into blister-like skin inflammations.