There is no real way to to tell for sure what type of insect is biting based upon a bite mark. You really need to find evidence of the actual insect to know what it is and how to manage it.
I would recommend that you put out some glue boards in areas where you get bitten and then submit them to a local Extension office, university, or pest management company for identification. You can also inspect the mattress and box springs for evidence of bed bugs.
Here are some publications that may help you.
Information on bed bugs:
Mysterious bug bites: