Off sick at new job, I’m worried I’ll get fired

I’ve been at my new job for just under 2 months, it’s been going so well but the last couple of days I’ve been feeling terrible, I’ve got a cold and I’m so weak and unwell, I went into work yesterday and they said I can go home if I want but I carried on until the end of my shift. However I went into work today and I was in for 15 mins but my manager said she thinks I should go home, so I said ok and went home, I’m worried they might fire me because I went home for being unwell whilst I’m still very new to my new job.

Do you think my employer is annoyed with me and could consider firing me?

Sounds ok, your boss encouraged you to go home and you don’t have a poor record in the albeit short time you’ve been there. Many organisations do have policies to discourage regular short absences, and these should be transparent. Agree with joining a union, a doctor isnt relevant for a short self-certifiable illness