I'm still learning myself, but that sentence seems a awkward.
It reads a bit more like "137 days is my japanese learning" since you've put 137 as the subject. It gets the point across but it probably sounds really weird.
I would probably write out that sentence as this (particles are underlined).
私
は日本語
が百三十七日間
に学んでいる
私は defines you as the subject and 日本語が defines japanese as the topic. As for 百三十七日間に I wasn't too sure about this, but I figured it's better to use the ni particle as opposed to the de particle, since you're partaking in an action with no definitive end-date.
学んでいる is a conjugation. The て form stem of まなぶ is まなんで, once you have that it's just a case of gluing on the right thing to the end, in this case, we add いる to make it non-past progressive tense.
Most of that sentence structure is just knowing the particles to use. て-form is a bit annoying though. I'm a lot more comfortable since I listened to
Miku singing the て-form conjugation rules to the theme of "Country Roads".