Hi, some suggestions:
First, it's just one drum, so might want to change all references to the drum to singular, or, should you have chosen plural for stylistic reasons perhaps, add a footnote. Plural of 'Trommel' is 'Trommeln'
'Doch als dann die Trommel rief' -> 'doch' means here 'but / yet / still' -> 'But then, as the drum was calling' (something like that)
'Hab mich nicht mehr umgeschaut.' -> I'd translate that to 'I didn't look back', it means that he didn't turn around to look back, and it fits the context for both lines.
'Denn die Trommel ruft so laut' -> that's present tense, so it should be 'Because the drum calls so loud'
About 'querfeldein' - I think you could perhaps also translate that to 'over hedge and ditch', I guess it means that he's just running and not paying attention which way he takes. That's it :)
suggestions are always welcome
vorschläge sind willkommen