I have had a similar situation with dc (also had sids in the family, and my dc had reflux and associated apnoea, which made it worse), and tbh although I never got totally over my anxiety no one else knows about it. Well dh does, as I have told him, but neither of the dc are aware and it is not an issue.
I had the dc with me for longer than you have, and afterwards I had a double bed in their room so if they woke up I could get into bed with them - I also did this if I couldn't sleep for worrying sometimes.
I am completely not an anxious parent and am actually fairly laissez faire about letting them take risks when they are awake - but them sleeping still terrifies me a bit.
Dc are now 10 and 7 and I still occasionally pop my head through the door before going to bed to hear them breathing. They occasionally get disturbed, mutter 'love you mummy', then turn over and go back to sleep. Ds1 has told me he likes the fact that I sometimes give him a cuddle in the middle of the night (which I do when I can't hear him breathing through popping my head in the door
).
I think that you need to do what you need to do to manage your anxiety, so long as it doesn't negatively affect your dc. Everyone else can go hang, imo.