You're right that you are probably inhaling the pesticides while spraying is going on but you could also be inhaling them even when spraying is not happening, just not as much. What the effects on you are depend on what is being sprayed and how much you inhale. Here is a website for you to look at http://members.aol.com/rccouncil/ourpage/samples.htm#class
Because you don't know what is being sprayed or how much you are inhaling, you probably shouldn't run near the fields while they are being sprayed. Especially if you see the workers wearing gas masks.

The answer to your question depends, Jesse, on a couple of things.

1) The type of pesticide being sprayed and the concentration being applied. This also includes the amount of time that they spray.This will also relate to its persistence in the environment (ie. how long it remains) and how toxic it is.
2) The time of application and correspond that with the time you run at.
(ie. are they close to the same time?)
3) The sensitivity of each individual to the pesticide. This is hard to measure, but certain indivduals are more sensitive to a lower dose of pesticide.

Some pesticides are easily transported into your body's system via inhalation, ingestion and topical application (ie. it has to come in contact with the skin). Lets assume that the pesticide does some how enter your system, since some kids always go home sick. The short term affects are pesticide-specific--dizziness, depression, tremores, headaches, nausea, vomiting and some of the more detrimental effects can be cancer, necrosis of some portion of the biological system (ie. skin,liver,kidney, etc.) to even death with large doses exposure or long term exposure.

Long term exposure is harder to prove--cancer is a good example as is death. The problem is that people usually die by some portion of their internal system breaking down....This is also an effect of getting old, or so we think. So it is hard to say did the person die because he was exposed to pesticides or some other chemicals for X amount of years or did he die because he got old? Some times you have to look into the family history about it. If nobody in the family has ever died because of a specific sickness or that sickness occurs statistically too frequent in one specific region then maybe it was some external action, which caused it.

This probably doesn't answer your question, but if I may ask you to observe the frequency of spraying, ask the workers what they are spraying or if you knew the crop, then look to see what pesticides are frequently sprayed on them. This could be done by a simple internet search and going to the manufacture's home page. Also the US EPA has a lot of info on chemicals, too.

I can understand why this would concern you. Like any good scientist, you have observed some facts (data): 1. spraying occurs near your school, 2. After running a mile, some kids go home sick. You have also made a hypothesis (guess): The pesticides are causing the illness. You have also hypothesized that the short and long term effects of a chemical may be different.

Your hypothesis that fact 1 causes fact 2 could be correct, but there are other possibilities too: running a mile when you are not used to it might make you feel sick; some kids might be faking it to go home early; maybe the kids think the pesticides are making them sick, so they feel sick. (This last hypothesis is the opposite of a "placebo effect" in which people think they're taking a drug, so the feel better, even if it's just a sugar pill.) The next step would be to test the hypotheses. This is the most difficult step. It would NOT be right to spray some kids with pesticides and make them run, and compare them with kids you sprayed with water labelled as a pesticide. Even though the answer would be the clearest, it would be illegal and unethical.

So what can you do? You could keep track of patterns. For example, you might secretly keep track of when the spraying happened and how many kids went home sick after each run, and see if there were a pattern. (Why would it be a bad idea to tell the other kids you were keeping track?) You might also collect other information like whether as many kids went home sick on days where there was going to be a test later on vs. when there was going to be a fun event later.

As you suggest, sometimes the long term effects of a chemical are different from the short term ones. Short term effects might include breathing problems, headache, nausea, or skin and eye irritation. Long term ones might include cancer, damage to tissues, or damage to genes (DNA). The specific problems would depend on the specific chemicals used and their concentration.