My wife and I are travelling for a few months. Several times my wife waked up explaining that she has been bitten by bed bugs, but I don't feel that I have been bitten. Why is my wife their only target? Or I have been beaten but I am not "allergic" to them?
Bed bugs are not usually target specific, if they are in a bed they bite anyone in that bed. The same applies for other non flying blood suckers like fleas, chiggers, ticks.
Flying blood suckers like mosquitoes, horse flies can be target specific zeroing in on certain people while ignoring folks sleeping right next to them.
Bed bug bites are rather easy to identify visually, follow the link in the comments above. Bed bug bites also tend not to be felt until you wake in the morning and start scratching them. If your wife is waking up during the night from being bit, mosquitoes are a more likely culprit.