You need to seek support and advice from your Student Union.
I think the first thing to check is what the university's policy is on dealing with attendance issues, to make sure it has been followed. I think it's unlikely that the first thing the university should do is to send an email withdrawing you from the course -- I'd have expected a process where they contact you rather sooner than 6 weeks of non-attendance, at least to enquire after your well being and offer support if required.
A three-month old doctor's note for a chest infection is probably not going to be much help now -- I know coughs can linger for a few weeks after a chest infection clears up -- but it's now 12+ weeks later, and if you're still having problems with that infection then I'd have expected another visit to the GP.
Can you provide the university with medical evidence of how your asthma is preventing you from going outside? With regard to coughing in lectures, then yes it can be a bit disruptive; but that's something that other people have to deal with. If it's sufficiently disruptive that you can't attend lectures, even weeks after you've had an infection, then again that's a sign that you needed to see your GP again.
You'll need to read your university's policy on attendance, and bear in mind that most universities don't offer remote learning programmes. Covid forced universities to move online out of necessity; but now that Covid is much less of a problem, things are largely back to "normal" in terms of an expectation that students will attend classes and other academic commitments in person.