No, no, no, OP please ignore my last. I'm so sorry, I'm confusing the issue. That's from writing a post too quickly as I was in a hurry. I'm really sorry :(
You can ADD to a batch on the same day (ie within a 24 hour period), recording it as being expressed at the time/date as the OLDEST milk in that batch. Cool new milk before adding it to the old. You don't have to combine it if you don't want to, it's also fine to keep each batch in a different container (labelled).
You can then freeze it or keep it in the fridge for 3-5 days depending on how cold your fridge is. See here for info on that:
www.breastfeedingnetwork.org.uk/pdfs/BFNExpressing&Storing.pdf
(this is the leaflet Badger linked to above).
Now, let's look at this from a different angle. Firstly, have you double checked that you can't take the drugs you need while breastfeeding? Most drugs aren't tested on lactating women, so doctors generally say you can't take X drug while BFing even though in fact it's ok. So, it's worth checking that out. Here's the link for that: www.breastfeedingnetwork.org.uk/drugs-in-breastmilk.html
If you can't find what you're taking in the list, call this number: 0844 412 4665
Assuming you find that it's not a safe drug to take while BFing, let's look at ways to express more milk. You are sounding so upset, and this will possibly impact on how much you can express. Can you take yourself off for a walk, calm down, enjoy the grey weather
, get rained on and play in leaves? 
You are not running out of milk. Your breasts may feel empty - may not express milk - but they are producing it and your baby will be able to get the milk out. Letting him finish one side, then moving him over, then back again to the first (as many times as required) will let him keep getting the milk that your breasts will keep making.
It's worth, if you can juggle it, trying to express while feeding. This often produces more. Try to get really comfy with cushions to suit. It may be easier to have bub in a rugby hold as it gives you clearer access to the other boob. Top tip - get your telly channel set up first as you'll have no hands free
.
In the end if you do find it's not possible to express enough for 24 hours, and you don't have a lactating friend who you'd be happy to accept donor milk from then it's ok to give formula for 24 hours. Really. :)