OP I agree that you need to speak to your line manager. Your employer should have policies in place: we have been open pretty much throughout and we have lots of covid policies now. It sounds like your employer does too given that you're distanced from each other and wearing masks.
One of the policies we have is that if we have covid symptoms we need to self isolate and have a negative PCR test before we can come back to work.
In fact isn't it national guidance to self isolate and test if you have symptoms?
This guy has symptoms and therefore needs to self isolate and test. Hopefully he has done so and tested negative which is why he's in work. We can go to work with coughs etc but we need a negative PCR.
Obviously you can't ask him as it's not your place. But in the circumstances I'd say it's fine to speak to your line manager and say that you've noticed a colleague has covid symptoms and you are worried about contracting it. They can then make the necessary enquiries and act/reassure accordingly.
Part of their duty to you as an employee is to not put you at risk and part of that duty in turn is to ensure that any covid policies are followed.
So that's the practical steps you can take. In terms of managing your anxiety, I guess utilise whatever coping strategies work for you when you are feeling anxious eg distraction, grounding or whatever. Listen to music, do breathing exercises, whatever helps.