Insect Bites or Other?

I have noticed several small red bumps on my skin, mainly on my arms and legs. I think I am getting these when I am sleeping but I am not 100% sure. They look like small insect bites. I called in an exterminator but he could find no trace or evidence of bed bugs. I also went to the doctor and he could not say for certain what was causing them.

Does anyone have any idea what they might be? Could it be mites, some kind of allergic reaction, or something else?

First of all BEEN THERE there is no recorded evidence of spiders ever biting people in their sleep, except for the rare cases when you might roll over on one, which in any even would kill the spider, and you would see it in your bed the next morning.
That is one misconception that can certainly stop being spread around, there are no parasitic spiders, they are all predatory and feed on other living organisms, insects or others.
It is possible that they could be mites, although mites are still visible apon close inspection.
Lice is another common possibility.
Bed bugs was my first guess until you said that they could not see any. Bed bugs are usually quite obvious. They leave dark patches which are their feces all over the edges of matresses and couch cushions, this is what gives away their location in most cases, but if it is not that then it could possibly be some sort of reaction to dtergent or fabric softener.

could be scabies - although this usually starts on the hands. Could also be spiders. They tend to hide at the bottom of your bed and creep up at night. Wash your sheets - spray your bed with a bug spray (if you're not allergic) and if you are - try a product called 20 muleteam borax - (in the detergent aisle) - This is also good for ants, etc.