I am going to school on foot now.

I am going to school on foot now.
今天上英语课时,英语老师让我在黑板上写“我现在步行去上学”,我便写下了“I am going to school on foot now.”没想到老师竟来了一句："这句话是一个病语.Be going to是一般将来时,now又是现在的意思.应该改为I go to school on foot now.这让我感到可笑,我是用现在进行时来写这句话的,又没有范语法错误,难道是因为我记错了?还是老师出错了.即使我不应该用现在进行时来写,老师也没必要说我写的是语病啊!
不是选择时态对不对,是有没有语法错误!