How can I deduce the structure of my compound from this NMR spectra?
The hydrogens in the structure you drew definitely should not be in the same environment — so while overlapping or close signals would be okay, the way your signals look isn’t. To get two signals to be identical, there needs to be some symmetrical way of corresponding the hydrogens to each other.

I can confirm a trans-configured double bond (I assume you can, too?) and two disubstituted aromatic rings. The question remains which type of substitution they have (ortho, meta or para). If you expect two rings with the substituents you drew, remember they must be pretty different in their chemical shifts!

For ortho, as you drew, one would indeed expect a set of doublet, triplet, triplet, doublet for each ring. meta would expect one set of doublet, triplet, doublet and a singlet somewhere. para, finally, would expect two doublets.

Remember that triplets must have a $1\,:\,2\,:\,1$ ratio, or they aren’t triplets. With this information in hand, go back into the aromatic region and think what you could have gotten. I have dropped enough clues, I hope.