If I may say so, "I am walking through my garden" is not a particularly English thing to say or do. I don't think native speakers say this at all.
I am walking through ... means "conducting a tour of inspection (to see if there are problems or imperfections)". It does not mean taking a walk in the garden. 我在检查我的花园。
On the other hand, if you have something like, "As I was walking through the Luxembourg Garden, the German bombing started", 那是可以的。 我刚要从(巴黎)的卢森堡公园从一头走到另外一头的时候,德国战机就开始空袭了。这是某一时某一地的历史语境。
"我在花园里散步", 要是用英语来形容这个情景, 我们会说, "I am taking a walk in the garden", native speakers 根本很少说 "I am taking a walk in my garden", 就连这个"my garden"也很少用在"I am taking a walk in the garden", 尽管你正在自己的花园里散步。还有,要是花园不大, 也不会说"I am taking a walk in the garden". 要是花园很小,只是屋子后边一些余地而已,不管是多精美,也只会说: "I am having a stretch in the garden". 光是说在花园走走,英语也有很多不同的语境的。Mastering a language involves understanding nuances and cultural habits. 所以随便找句英文句子来翻译, 并不是学习汉语的好方法。首先,那句英语可能已经是错漏百出,然后英语的思维和英语世界的生活习惯跟中华文化的生活习惯也不一样。学汉语,最好是全心全意投入汉语的世界里,千万别幻想: 我要不要借助另外一个语言,作为桥梁,来走近汉语。