Already put two comments but ideas keep coming to me so I'll just package them here. Keep in mind I'm not an educator, I'm just trying to think of practical solutions to the problem as a whole.

Another answer recommends YouTube to upload source material but I feel this might be inadequate interaction. Other alternatives:

Discord

Recently in response to COVID, they've upped their free screenshare capacity to 50. The first approach could be assemble a small top-down view from of a portable whiteboard that you write on during the explanation. Something like here. You'd have to position a portable webcam to achieve this. Discord also has slack-like text and speech channels that you could maybe host discussions about dedicated topics. E.g. Algebra Channel or Calculus

The issue with discord is that while you can stream/screenshare to those present, the stream media isn't archived which can be useful for future reference. However a service that does:

Twitch.tv

Although primarily used for entertainment purposes, I think you might be able to use it in your situation. If you still have access to your faculty building you could use an empty lecture theatre's whiteboard and effectively "stream" a lecture free to Twitch. Set up your laptop on a desk at the front, start streaming and conduct the lesson as normal. This has the added benefit that Twitch archives your past broadcasts so your students can use it as a reference repository in the future.

Another potentially useful feature is that there is a chat sidebar so that your students can ask questions which you can answer in real time should that be necessary. It's not the most formal of arrangements but needs must.

If you are concerned about privacy, I'm pretty certain you can restrict public access to private links you can distribute to your students.

P.s. I find it most strange that your faculty isn't helping you either financially nor in regard to helping you come up with a working process.

Already put two comments but ideas keep coming to me so I'll just package them here. Keep in mind I'm not an educator, I'm just trying to think of practical solutions to the problem as a whole.

Another answer recommends YouTube to upload source material but I feel this might be inadequate interaction. Other alternatives:

Discord

Recently in response to COVID, they've upped their free screenshare capacity to 50. The first approach could be assemble a small top-down view from of a portable whiteboard that you write on during the explanation. Something like here. You'd have to position a portable webcam to achieve this. Discord also has slack-like text and speech channels that you could maybe host discussions about dedicated topics. E.g. Algebra Channel or Calculus

The issue with discord is that while you can stream/screenshare to those present, the stream media isn't archived which can be useful for future reference. However a service that does:

Twitch.tv

Although primarily used for entertainment purposes, I think you might be able to use it in your situation. If you still have access to your faculty building you could use an empty lecture theatre's whiteboard and effectively "stream" a lecture free to Twitch. Set up your laptop on a desk at the front, start streaming and conduct the lesson as normal. This has the added benefit that Twitch archives your past broadcasts so your students can use it as a reference repository in the future.

Another potentially useful feature is that there is a chat sidebar so that your students can ask questions which you can answer in real time should that be necessary. It's not the most formal of arrangements but needs must.

If you are concerned about privacy, I'm pretty certain you can restrict public access to private links you can distribute to your students.

P.s. I find it most strange that your faculty isn't helping you financially nor advising you on the faculty process of teaching going forward.