Are the chemicals bed bugs inject into you causing diseases?

It really depends what you mean by "disease" but basically everybody is different on this. The chemical a bedbug injects into you (usually when it feeds off your blood while you are fast asleep in your bed at night) consists basically of an anaesthetic to prevent you feeling the insect's presence on your skin or feel the sharp piercing of your skin to extract your blood and an anticoagulant to stop the blood coming out of you too fast for the 5 minutes or so while the bedbug's stomach is being filled with your blood.

So when you say "disease", the point really is the chemicals affect different people in different ways. While bedbug bites do not generally cause any serious disease (like mosquito bites can cause malaria), being bitten by bedbugs do cause considerable irritation to some people. Some individuals get itchy blisters or welts or red blotches on their skin. That is usually because the individual is allergic to one or more of the components in the chemical that the bedbugs have injected into them.

The marks on the skin which may be on your arms, back, shoulders, legs and/or face take different forms on different people. With some the marks may appear on the person's skin within an hour or two usually but not always accompanied by intense itching, or in some cases a day or sometimes not for several days after the bedbug has completed its meal. Others bitten by bedbugs seem to suffer no such effects, and in some cases may get bitten night after night by bedbugs who live in their bedroom without ever realising what is happening to them. Some people suffer no unpleasant effects whatsoever from having bedbugs in their bed.

BUT with others a long term effect of being the victim of a major bedbug infestation in their bed, and having their blood extracted night after night can in extreme cases be be anaemia. This can cause a reduced level of the oxygen carrying pigment haemoglobin in your bloodstream. That can lead to a deficiency of B12 or another vitamin, folic acid. That in extreme cases can cause you to be habitually tired, frequent headaches, a sore mouth and tongue, weight loss and/or jaundice!, and in some cases the problem might possibly be the victim just does not realise why.