I am not competent in the question, but I'm native speaker :)
So, lets try to make these sounds. First of all, I hope you know english sounds CH and SH.
Russian Ш is almost the same as english SH.
There are no sound as Щ in English. But you can stretch out english СH ( Ch-h-h-h-h... )
So, beginning of this stretched sound will sound like standard CH, but the ending will sound like russian Щ.
Note the position of you tongue while making these sounds. In case of SH your tongue is above, but in case of CH your tongue is at the bottom. Then repeat sound SH but hold your tongue in position of CH and then practice, practice and more and more and more...
I think the position of the tongue is the main difference of these sounds.
I think so, but I am not sure.
With best regards, Sasha.