Yikes mum, that is unfair. I had blocked duct and was terrified of mastitis, yup to feeding/ expressing lots, but also rest (!) and hot compress/showers and ibuprofen. Do done googling to see what is recommended, but mine cleared in a day or two. I didn't drain it every 2 hours, so perhdosctou could just offer it with nipple shield when you know babe is really hungry and likely to drain it, then start next feed with other breast and express a little from painful side if poss, then repeat... Try different feeding positions as well as that seems to help. What rotten luck, sorry. Let your DP know he must reeeeally help out to stop it turning into mastitis- look after other DC and bring you everything you need while feeding (including hot water, flannel and towel for hot compress - best to do 15 mins before feed I think, followed by some breast massage to help clear blocked area.
From body towards nipple)
Good luck!