There is a very long list of symptoms experienced by astronauts, some of which are related to the microgravity environment and others that are caused by something else. Determining exactly which causes what isn't always straightforward.
In microgravity, blood pools more in the head and upper body than it does on Earth, where gravity pulls it down to your feet. Similarly, the internal organs move upwards towards (or into) the chest cavity. Lying down also removes this gravitational pull towards your feet, so you'd expect the same thing to happen .. except...
Lying down isn't the same as being in microgravity. Imagine a pea in a glass tube. In microgravity, it will float, and a gentle breeze through the tube will cause it to move along the tube. If you lie that tube down on its side here on Earth, however, friction with the tube walls would prevent it from moving.
That said, lying down IS a good analogy for being in microgravity for a lot of conditions, even if it isn't perfect. In 2014, NASA conducted a 70-day bed-rest study, called CFT70, to "test the effectiveness of exercise on loss of muscle, bone and cardiovascular function". As @PearsonArtPhoto has already commented, you can find a first-person write-up of that experiment over at Vice. This wasn't the first such experiment, and it probably won't be the last, either. Some of the results from such studies might surprise you, such as the effects of lying down on your senses of taste and smell or even structural changes in the brain.