A wonderful thing!
I am so glad you held on and did not give up!!!!
Yes! they can fight in miraculous ways. They can also go without breathing for hours on end, unless they have the indications of death (won't get into it)
Waiting it out was a very wise choice

I just went through a similar experience. It was a long, long, long tough road (14 weeks) but she made it through.
As for the meds - have to give a disclaimer: self-prescribing is risky.
What antibiotic are you thinking of?
Please keep in mind that my vet meticulously calculates dosage - for example a difference of 20 grams in weight required a change in dosage.
At the age/size of your little one, you will need to administer them via injection, so you will need an appropriately sized syringe needle and will need to know where and how to inject the medication.
I am talking in circles, I know...
I WANT to give you an answer, but would be remiss if I did.
I did a quick search on the forum for posts from others in the Philippines - I found one posted 2009 from someone looking for a vet in the Philippines. I did not check out the link, I do not know what it says/offers, but maybe you can find a number to call or something:
http://www.vetworld.com/vetworld/philippines.html Keep us posted!