Context on using available vs accessible

Accessible implies that it is not only available but in a place where it can be accessed. Something might be available but not easily retrieved; accessibility implies some ease of retrieval.

"Avail" as a noun means "beneficial effect; advantage, benefit, profit" (n. 1a). To "avail oneself of" something is "to benefit oneself or profit by; to take advantage of, turn to account" (v. 4). A resource is "available" if it's possible to take advantage of or profit by it.

To "access", on the other hand, is simply "to obtain, acquire; to get hold of" (v.2 1a), or "to gain admission to; to enter" (v.2 1b).

The difference, then, is that "available" emphasizes the benefit of profit someone may derive from using a resource, whereas "accessible" has no such connotation, and emphasizes the possibility of obtaining or reaching something.

In many cases, "accessible" and "available" would both be appropriate, and the choice would only depend on which word's connotation you found most fitting. In the example you give, it's certainly not wrong to speak of the medicine being "accessible" to everyone (incidentally, "accessible to" is more common than "accessible for": see OED "accessible"). In this case, however, I would use "available", because the point is that the medicine is a resource everyone should be able to benefit from; the physical mechanics by which each person gains access to the medicine are irrelevant, provided they can use it.

By contrast, a building with a wheelchair ramp is said to be "wheelchair accessible", not "wheelchair available". The reason is that the issue here is whether a person in a wheelchair can physically get into the building, with no reference to whether entering the building is a source of profit or advantage.

Source: OED

Medicine might be available for your children but not accessible to them. Its availability indicates the possibility and profit of its use by them, while not being accessible indicates their inability to obtain it on their own.