I strongly recommend that you go to see your primary care doctor
about this issue. They can examine the spots on your skin and help you figure out what might be going on and whether or not you need to do anything about it.
The most likely possibility for these 'brown spots' is that which you have already suggested, namely that they are small bruises. Bruises, when they first occur, are often reddish purple in color, but as the blood inside the bruise
is digested away by the body, they often fade to a yellowish or brownish color. They are also often sore to the touch when you press on them.
If your doctor takes a look at these spots and confirms that they are bruises, then there is likely nothing you need to do in particular to treat them. However, if all of these bruises are a new thing for you, then it will be important to figure out if there is a medical condition underlying the reason why you are suddenly experiencing frequent bruising, such as low platelets in your bloodstream or trouble with your blood clotting.
Depending on what your doctor finds, he or she may wish to perform some basic blood work to look at these issues.