Why was しよう used instead of して？
I was thinking して because it appears to be a request.
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I think the translation, plainly and without any other context, is:
Let’s follow this account and (then) check the photos and videos.
The volitional form used on its own has the meaning of “let’s”, and applies to the whole phrase. The earlier して is acting connectively.
して mid-sentence cannot, to my knowledge, be used as a contraction for してください, because the (much) more common use of して is the connective form.