Not feeling good after a ride
First off, can you explain a bit more about how you "don't feel very good"?  Do you feel at all queasy?  Do you feel especially weak?

Also, how often do you exercise so intensely, and how long have you been doing it?

And how long does this period of feeling unwell typically last?

Anyway, there are several possibilities (though most apply to rides longer than 15 miles):

-- Dehydration.  Especially in warmer weather you need to drink plenty of water or other fluids.  We've had arguments here as to how much, but it's not a bad idea to down a 21-oz bottle of water every two hours or so, as very rough guide -- more in hotter weather.

-- Low sodium.  Again, in warmer weather it's quite possible for someone who exercises intensely to sweat off so much salt that the sodium levels in their body are not sufficient.  (This effect can be doubled if the individual consumes an extremely low-sodium diet.)  This results in fatigue and lethargy, and in extreme cases can be life-threatening, especially if mistaken for dehydration (which has similar symptoms) resulting in "water intoxication".

-- Low blood sugar.  When you exercise you first consume the sugar in the blood stream, then the liver and muscles start converting stored glycogen to sugar.  Several other mechanisms kick in as well.  Especially in someone who has not trained extensively, this mechanism may not be able to supply the body with enough sugar and low blood sugar can result.  In addition, some people suffer from what's known as "reactive hypoglycemia", where blood sugar drops paradoxically after a meal, after exercise, or at certain times of the day.

-- Ketosis.  If blood sugar gets too low for too long the body begins to burn fat and protein directly.  This results in the production of ketones which are released into the blood stream.  This again results in an unwell feeling, including nausea, extreme fatigue, lethargy, and "brain fog".  (Ketosis in particular will knock you on your butt for 2-3 days if it gets bad.  Most other conditions listed here you can recover from in a few hours at most, if properly treated.)

-- Blood pressure fluctuations.  Some people experience fairly extreme changes in blood pressure after exercising.  This is usually short-lived, but can produce a wide variety of symptoms, from pounding headache to fatigue and fainting.

-- Neurotransmitter fluctuations.  It's well known that exercise (especially intense exercise) causes the release of a number of neurochemicals.  This is cause of the so-called "runner's high".  And, of course, when one is "high", one will eventually "come down", and the result is a sort of "withdrawal" from the endorphins produced while exercising.

My guess is that you're experiencing a combination of slightly low blood sugar and the neurotransmitter "withdrawal", maybe combined with a touch of dehydration.  Eating some sweet or starchy snack every 30-60 minutes while riding will help to level the blood sugar (and if it's a bit salty, all the better). Drink a cup or two of water with the snack.

And when you finish the intense part of the ride, take a leisurely spin around the block or whatever for 5-10 minutes to "cool down" -- not your temperature so much as your endorphins.

(You can, of course, experiment with different combinations of the above to try to narrow down what's the primary cause of your particular symptoms.)

But (though the doctor's checkup is never a bad idea) I wouldn't worry about it too much.  After all, you've just participated in the second-best activity a man can experience, so a little let-down afterwards is to be expected.