(repost since i mistakenlly put it as a comment)

今週、私のリサーチは始まりました。だから、私は忙しいです！私のエセジの遅いでした。でも、私のリサーチは面白いです！

【今週、私のリサーチは始まりました。Its not bad but if you are going to use は you better explain what your research is about after this sentence. This sentence sounds like a dramatic narration in the movie】
今週、私のリサーチ<が>始まりました。

１．だから、忙しい！(it sound a bit pushy as私は忙しいです can be but more natural. But people would think you are hurrying or irritating)
２．だから、忙しいのです。(natural, but it could be pushy since it sounds like “yes it’s obvious but I’m busy”)
３．だから、とても忙しい！(very natural Japanese. Its better to put an adjective to make it flow, so the word “very” is added here)
４．だから、（最近）忙しくなりました。(I became busy. Natural. I recommend adding adjective for the 忙しい here too so I added “recently” for this sentence)

私のエッセイ<が>遅い<の>でした。(what is essage? Maybe we could help you if you could explain it for us)

【でも、私のリサーチは面白いです！ “But, my research is interesting!” is ok, but pushy and sounds like a kid so let me help you here too】
１．でも、私のリサーチは面白いです<よ>！ Suggesting it’s interesting to the reader
２．でも、私の<している>リサーチは面白いです！ What Im doing(research) is interesting! している is used to express the “ing” and makes the sentence natural and flow

Some Japanese tips: we usually drop down the subject(like 私) a lot.
今週、私のリサーチは始まりました。だから、★忙しいです！★エセジの遅いでした。でも、★★面白いです！like around the stars(note: im not correcting the grammar here)

And let us know what your “research” is. Is it an experiment or writing a research paper? Because the Japanese for the “research” would change with what you are doing.
実習、実験、研究、卒業論文etc… or maybe it cannot be explained in one word. Maybe it needs to be in a sentence to describe it.

My English is very rough but hope this would be some help for your Japanese.
リサーチ頑張ってね！