As much as I want to champion this, Monzo is still a beta prepaid card. It has always been recommended to not carry it as your only card to avoid these exact types of situations. 
Customer services reportedly being of no help sounds like something @emma_mondo might want to take a look at.
I do agree that there should be some more notifications about limits, however the whole model of limits and their amounts is about to potentially change with the rollout of the Monzo current account and full debit card.
Limits themselves are certainly visible in the app and it’s possible to get higher limits in two stages, the first is identity verification as shown in the following video that @Naji produced. (On Android, the limits are shown in a similar place.)
The second stage limit raise is quite recent and is explained in this post. The full eligibility criteria hasn’t been made public but it might be worth asking if this can be checked for your account.