There are some red flags sign for sensory issues as you have mention in your question but we need to do complete history, routine, play behaviour assessment and sensory evalve to know the issue. For running around and head stmming, deep pressure will be very useful. It helps calming child. Since you have not mention age i will give general activity like wrapping in blanket below neck, tight hugs, pushing and pulling activity.
Next Steps
If your not able to reach to centre due to COVID situiation do not delay assessment and therapy. Opt for teletherapy.
Health Tips
Age is very important factor of sensory integration therapy. Although neuroplasticity (brain remodelling) happens throughout life span, its best at young age so do not delay.