I’m pretty hopeless at this and keep getting killed by the skeletons down in Bleak Falls Barrow.

Does anyone have any tips or advice as to how I can get through this part?

Thanks

If you're really struggling then try adjusting the difficulty or get out and level up a few times concentrating on your combat skills before trying again. The dungeon will have locked in at the level you first entered so going back later should be easier.

Stealth bow shot > run away till hidden > shoot again.
Any posions that do additional dmg can help.
Silver swords do epic dmg on draughs and skeletons.

What difficulty are you on? The regular Draugr are some of the easiest enemies in the game.

Try turning the difficulty down.

What weapons are you using?
The key to dealing with any bad guy with melee (non duel wield) is to block, bash, stab! Why Block means they do negligible damage bash = they get staggered & you can get in ~2-3 hits with out any danger. Also use Power attack if they are blocking it breaks the block and staggers them.

BTW Blunt weapons are best for this at lest at start due to the higher base damage rocks.