I have just lowered the stem on my road bike. The headset components might not be installed correctly. Whenever I hold on to the front brake (making sure the wheels aren’t moving), and rock the bike back and forth, I can always feel something unstable. Are there anyways I can fix this problem?
By 'instability' let's assume you means something feels loose, and you can feel play on the the handlebars or fork when you rock the bike with the front brake held on.
The first thing to do is isolate where play is. Its likely between the bars and the fork steerer tube or the steerer tube and the frame. Hold the frame steady and rock the bars. Hold the front brake on, grab the headtube and and rock the frame, You should be able to tell where the play is.
The fix depends on whether you have a threaded steerer and quill stem, or an un-threaded steerer and clamp-on stem. The latter system is ubiquitous these days except on cheaper bikes.
If you have a un-threaded steerer and clamp-on stem, the stem holds the whole system together so if the stem is loose the headset bearings are loose. You probably did not have sufficient tension in the top cap when you tightened the stem. There are plenty of guides online that show you how to set preload tension in the headset bearings when the stem is installed or adjusted.
If you have a threaded steerer, if the stem is loose, just tighten it. if the headset bearings are loose they can be adjusted easily. Again there are plenty of guides online that show you how to do that.
Here's something to get you started: