I think this is the fun of a mage.
Mages are hugely overpowered as soon as you have unlocked duel wielding and the knock back perk (which you can do almost immediately). You can destroy anything one on one (just did the main quest and tbh I broke it because the fight was just ridiculously easy, Alduin got 1 attack off and then died to knock back).
BUT when fighting multiple enemies things get exciting. Because if any melee gets anywhere near you, you will get 2/3 hit and archers just get progressively more dangerous as you level up. I think its great balance to be offensively a god but defensively useless

Some things that could help you:
i) rotate through multiple enemies to ensure they are staggered at all times (frenetic, especially with distant archers)
ii) start conjuring to get something tanking infront of you
iii) experiment with other spell schools e.g. calming
iv) start using light armour and levelling in light armour (although I don't like this from a RP perspective, there is no penalty for mages using armour, you could go heavy if you really want to rip the game).