Is it alright for a person that has had covid (about a month ago) and has an immune system to go outside when his family members has just got it?

Yes. You SHOULD be immune to new infections and can go outside. But, don’t forget, nothing in medicine is absolute. It’s unlikely you will be re-infected, not impossible. Should you begin to feel ill again with respiratory or gastrointestinal symptoms, check with your doctor for possible repeat infection.

IF you are experiencing symptoms, such as cough, fever or shortness of breath, please see your PCP and arrange for a COVID 19 screening test. Reinfection is possible but not likely. It is best to continue to wear a mask and use social distancing when outside. Continue to monitor your temperature, drink fluids and follow up with your Pediatrician.

You are concerned that you could be a carrier and you can transmit the virus to other people. Recent studies showed fully vaccinated people (it is called natural immunity in your case) are less likely the host and they pose very little risk to other people, but still possible in theory. So you should wear a mask for 10-14 days when going outside to be safe for other people.