有一只绵羊在河边用英语应该怎样说呢?

There is a head of sheep near the river.
sheep并不是不可数名词,而是集体名词,单复同形.
但是单数并不能直接说a sheep,要说a head of sheep 一头羊
就像cattle也是一样.

There is a sheep near the river
再次注意，绵羊是可数名词，只是单复数同形而已．

There is one sheep along the river可以．

There is a sheep near the river.
上海版牛津英语教材2B教材听力中就出现了a sheep的说法。
你的老师讲的不完全正确。
sheep的复数形式不变。
一只羊a sheep 五只羊five sheep

There is a sheep near/beside the river.
sheep单复数相同.

There is a sheep near the river.

There is a sheep in the riverside.