Many times, it's not just about copyright problems. I don't know much about copyright laws but yes it can cause problems.
It's about your reputation too. Would you want a logo similar to another brand's logo? Would you want someone comment on your logo that he/she has seen very similar logo somewhere else? Likely no.
You current logo isn't an exact copy unless you intentionally are trying to make it same. It is possible, but less chances that two designers end up creating exact same logo design. It has some variations in how the shapes are cut at a different angle. Your h is has one extra corner.
Also, h shape is rough (I don' know what's the purpose of it. Is that intentionally rough stroke? Is it showing some silhouette maybe?)
I've seen many times known brands using similar logos (in terms of structure). For example, I often wonder if this cigarette brand could sue Microsoft. It was a cigarette brand I had noticed when I was a kid. Later I realized structure of 4 squares is quite similar to current Microsoft logo.
But I guess it wouldn't cause much problems as both companies have different products, different values, different services. I mean they shouldn't be compared at all. Moreover, the structure isn't exact same. There are differences in proportions.
You can see Microsoft logo on this page.
It's okay to love your first draft and end up finding same on Google. I would execute some of more of your sketches and see. There can be many more possibilities. You never know you could find even better solution.
Personally, I would try a few new approaches (unless that rough h stroke you have created, has some special meaning, as it distinguishes itself from others). If I like the current structure, I would experiment more with it so idea remains same but still very much distinguishable.