[I] was wondering if I were to go to the GP now is there any way they could tell that I was sick these last couple of days through some kind of blood test or something?
"Food poisoning" covers a vast number of illnesses, and whether it is detectable after your recovery depends on what type of illness caused it. For example, if your gastroenteritis was caused by a norovirus (formerly called Norwalk virus, the most common cause of food poisoning), a blood test for IgM (Immunoglobulin M) to the virus, indicating a recent illness, might be positive.
However, diagnosing after the fact in a short term and self-limiting illness like norovirus infection is harder than diagnosis during the illness (which requires just a small stool sample), unless the pathogen is known with certainty, and even then, there may not be a residual response to test.
Clearly, you will be paying for a large number of tests with only a chance that one of them will come up positive.
In terms of getting a doctor's note, it's best if you a) have a prior relationship with the physician, b) call him while you're sick (not after) or c) see a health care provider, go to the school health clinic, a walk-in clinic, or something similar.
Writing a note after the fact is a tricky area ethically. Many doctors who know and trust their patients will do it without hesitation. But I can understand others simply refusing the request for a post-illness work-up (which might be negative regardless) on the basis of cost and questionable need.
Or to use a medical metaphor, an ounce of prevention is better than a pound of cure.
Antibody Test To Detect Genogroup II Norwalk-Like Virus Infection
Assessment of a rapid immunochromatographic test for the diagnosis of norovirus gastroenteritis.