Since the moon's gravitational pull is obviously strong enough to move oceans around, it does seem like it should be affecting our bodies as well. It turns out that it doesn't, though, and there are basically two reasons.

The first reason is the distance to the moon (about 385,000 km). This is a pretty big distance. Now, gravitational pulls get weaker with distance, and this is the reason tides occur. At any given time, one side of the Pacific Ocean (let's say the California side, for the sake of argument) is going to be closer to the moon than the other side (Japan). So there is a stronger gravitational pull on the ocean in CA than there is in Japan, so we get a high tide in CA and a low tide in Japan. Later in the day, the earth has rotated, Japan is now closer to the moon, and there is a high tide in Japan and a low tide in CA (obviously this is an extremely simplistic explanation of the way tides work, but you get the idea).

The reason we see a difference in the gravitational pull between CA and Japan is that those two places are pretty far apart relative to the earth-moon distance. If we try to think about tides in your body, we'd have to imagine that at some time there was a stronger gravitational pull on your head than on your feet.

Now, your head might be a little closer to the moon than your feet, but only by about a meter or so. The difference in the moon's gravitational pull between your head and feet is obviously going to be a lot less than the difference between California and Japan; in fact it's so small we can't even notice it. However, the difference in gravitational pull between your head and feet is real, even though it's very small. If that were the only force acting on your body, then you might notice it.

Luckily for you, there are plenty of other forces acting on the water in your body all the time. Aside from the earth's gravitational pull, you've got all the bouncing and sloshing and bumping that you get when you're walking or riding around in your car, plus your heart is pumping all the blood in your body around at a pretty high pressure, and even on a cellular scale, most cells are constantly letting water in and pumping it back out. All of these forces are a lot stronger than the very small force of the moon's gravitational pull, so the water in our body responds to them but is hardly affected by the moon. The existence of all these other forces are the second reason that the moon doesn't affect the water in your body very much. Hope this helps.