Hi Smudger,
One possibility could be that you have a faulty pen - are you seeing the level of Byetta in the pen reducing with each injection? Or possibly there is something wrong with the Byetta in your current pen - has it ever become overheated or frozen? Was it kept refrigerated until first use?
If it's not the Byetta then the next area to consider is your diet. I know you said you eat a healthy diet, but what exactly is healthy? If you are following the government's recommended "healthy" diet (which doctors and dietitians feel they have to promote as they are paid by the government), then you will certainly find your BS going up because it may healthy for a non-diabetic (debatable!) but for a type 2 is pretty much a guarantee of increasing BS. Bearing in mind that what you eat is what causes blood sugar to rise, the only way your BS level can rise is if you are eating more carbohydrate than your medication can cope with, or the medication itself is faulty.