How do I know if my anxiety is hurting someone else's mental health? How do I help it if it is?

Talk to them about it, ask them how they feel and encourage them to be honest and open about it. If it is hurting them, ask them what they need in order to be in a better mental place. Personally, I've been in both positions, and the best thing for both of us when I was helping a friend, was for me to take a short break from talking to them about their mental health so I could focus on my own. When we came back to it, we both agreed that I would tell her whenever I began to feel this way again, so she could help me too, and our relationship was the best it had ever been because we were both coming from a more open, honest place.

I once had a friend who was always very positive. At that time I was suffering from anxiety and depression. I soon realized that I was affecting her mood due to my attitude because she appeared visibly tired after conversations with me. I started asking people if they had the emotional space to deal with problems before I started discussing any sensitive issue. This helped a lot since people were mentally prepared for the content they would hear and could excuse themselves if they weren't. That way they could help me out with my problems while staying in the frame of mind they wanted

I know that my anxiety is hurting someone else's mental health when they take on my emotion and worries as their own. I can help by working on myself and reducing the source of my anxiety. I will explain to them what steps I am taking. We can openly communicate and express our feelings, hopefully receive help from a trained professional. I can help them by reassurance, being kind, compassionate, empathetic and stay by their side during the rough patches. My anxiety should be mine alone, however I could be hurting someone's mental health if they have a low capacity to take on other people's problems.