Like expatinscotland, I would like to say something about that as well... Well, not about being ill in particular, but about the whole thing.
Breastfeeding is not easy and in favour or against, for practical reasons or no, BF does not always cut out bottles. If it doesn't work because of the hospital, if you get cracked nipples, inflamation of the breast, if baby does not want to drink, you will need formula. You can better get prepared for it with your bottles and what not than think that that is the solution to everything.
At any rate, if people are recommending part-time jobs, which may be necessary to suport your family, how do they expct OP to breastfeed without bottles? Take the baby to her job? Right, express, of course. Fantastic, hello bottle! Ok, no formula, but halfway there almost.
And a sling... Can you picture yourself permanently carrying a three kilo (and more) wait on you shoulders, plus pushing a buggy while going shopping for your weekly groceries? I don't think I would get down to street without turning back due to pain all over. I think that is unrealistic in the long run. A small child of two can't walk a great distance and you can't carry a 5-10 kilo wait for more than 1 hour and that's pushing it.
The baby is bound to need a cot at some point so sleeping in the big bed is not a permanent solution either.
Get the father to pay maintenance. Surely, there is someone you can ask about even suing him (for free)? Otherwise the man is not worth the name 'father' and then he should quit seeing 'his' son.
And, yes, Ebay and other free websites, clubs. Maybe you could exchange your single buggy for a double one?
Good luck though.