Why shoulders feels tight, closed, injured, weak? Did you know our shoulders are the most mobile joints in our body which means it's easy for this joint to slowly wear and tear our bodies. Over time and age the ligaments (bone to bone connection)gets stiff. Our tendons (muscles to bone connection) wear the muscles become weak and short in length. Shoulders issues are common. One thing you should consider is mobility work. Mobility work is the most critical component for your body. It allows the joints to move safely with help the muscular stabilizer of the shoulders. Doing at least 10-15 minutes of exercises will help the supraspinatus/stabilizer muscles the scapula/shoulder blade, detoids, and many other mechanics in the shoulders. You can start by doing ROM (range of motion) as a warm up exercise, then strengthen muscles in the shoulders and scapula/shoulder blade. Lastly, add active and passive stretches for the shoulders.
I recommend reading Overcoming Gravity 2nd Edition by Steven Low it has major good points on shoulder prehab and rehab work. I had this book for two years now and it has helped me improve on handstand training. It also talks about how to construct a proper workout routine , gain flexibility and professional handstand mechanics. Below I have pictures teaching students exercises for opening the shoulders. I have a video with a few simple exercises to do that will help in arm balance and handstands.
Here is one of my student's doing an active stretching exercises to improve her Overhead Shoulder Mobility.
Here is a video on improving shoulder health for joint articulation and mobility for everyday life and not just for handstands only.