I'm gonna guess you're not counting carbs yet... If that is the case, i'd say don't worry too much yet, basicly you're not compensating for your Carbohydrate intake yet, so you're likely to swing a little bit or remain high (I was initially untill I started counting carbs).
Next time you see your Diabetic specialist, let them know what's happening (since I'm going on what happened with me) and chances are they'll say it's normal to to swing a bit.
As for the headaches, your body isn't used to changing blood sugars like that yet. Your brain needs glucose to function, if you start swinging (going from highs to lows quickly) your brain will be getting varied levels of glucose, causing headaches.
Just don't change your insulin intake quite yet, as your diabetic specialist will tell you all you need to know about the ratio of Carbs to insulin units and how to count carbs. Usually though, they'll keep you on a set amount for a week or so to make sure you get the hang of taking insulin. Your Lantus, usually (or atleast for me. and yes, I am on the same as you) doesn't change, that just provides an overnight 'background' of insulin to keep you going over night.
If you've got any more questions, feel free to message me, I'd be more than happy to help!