Fickle!

Any ideas or reassurance welcome:
My LO has just turned one and at the moment she is being really picky with her eating. She does seem to be teething and this does affect her eating but i keep serving up meals and she's just throwing it on the floor. She'll eat breakfast but very little after that and wont drink milk (she's been exclusively breastfed but only feeds before bed now-her choice!). Want i want to know is should I keep offering her different things (at the moment she only seems to want cheese!) or if she doesn't eat what i put in front of her should i just leave it. Am worried as want her to eat enough to keep her going but don't want her become 'picky' and always get what she wants. She seems healthy and happy (other than teething!) otherwise. Thanx xxx