One has to remember that cockroach bites, although technically possible, are extremely rare. Cockroaches are not like many insects that could inflict painful bites and stings. This is because cockroaches simply do not view humans as a potential food source or feel the need to bite us. They also will not typically pursue a human aggressively or bite out of any need or sense of self defense. Although they might look creepy, it must be remembered that cockroaches are not very threatening. However, there are chances of cockroach bites if there is a bad infestation of these creatures. This is more likely in poor hygiene conditions and places where overcrowding is a huge problem. If a place is crawling with cockroaches, you have to beware since there are chances that one of the many cockroaches might bite you when sleeping. This is because you might be viewed as a stationary object rather than a living being, when you sleep. The cockroach might take a nibble, especially if it finds any kind of traces of food, for example, on your face.
Cockroaches are infamous for their ability to eat all kinds of strange things. This is why hygiene in your surroundings as well as personal hygiene is indispensable. However, rarer than a cockroach bite would be the possibility of an allergy to it. At the same time, the subject has not been extensively studied. It has been noticed that children are more susceptible to these kinds of bites although, as mentioned earlier, this typically happens only when the cockroach population is out of control. There is a possibility of allergy, not in case of bites but in case of presence of cockroaches, on account of their droppings.
If there is a bump, as you would find in case of even mosquito bites, you should try to soothe the red area like you would with any other bite. It helps to clean the bump and this is usually done with plain water and a good quality mild soap. You can indirectly use ice since this is helpful in all kinds of situations where swelling is present. This will also help if you feel like scratching that cockroach bite. You need to hold back on scratching, since scratching any part of your body or any bite area is always inadvisable. If you do experience some kind of allergic reaction to the bite, you should always consult your doctor since it could be a bite from another insect or creature.
answered by G M