Would it be unreasonable to go to GPs to ask for antibiotics in these circumstances

[handlemecarefully]

Productive cough (yellow / green mucus) for 2-3 weeks duration. When I exhale orally you can hear a 'rattle'. It's not getting better

I don't feel really unwell but I am a runner (x3 weekly) and haven't been able to exercise for 3 weeks - which is depressing. Particularly since I am a fat fecker and need the exercise

Go and get yourself checked out.

if the mucus is dark I think it generally represents an infection as opposed to just viral, so can be treated with antibiotics - I think 3 weeks is long enough to know that your body is not fighting it off - go to quack.... I am very anti- antibiotics if you can help it though

Good - just don't like to waste the GPs time, but I really want rid of it

If it's green and not clearing on its own I think antibiotics are perfectly appropriate.