Try & learn the carb values of your most common meals, for example an egg sized potato =10 grammes of carb. Download a food database app to your phone if you have a smart phone (my fitness pal is one option). I agree with others, reduce your basal by a unit at a time if you keep going hypo more than 5 hours after eating. You may find then that you then need to increase your insulin to carb ratio which will reduce those highs after meals. HOWEVER do one thing at a time, otherwise you'll never know which adjustment worked.
DON'T WORRY about 12-14 after a meal for a couple of hours. It's not ideal, but some people (me included) can never get those values down, but still have overall pretty good control. You're very early in your adjustment/learning period it can take a few years to learn everything, it's a complex disease with many variables, it takes experience to consider them all at the same time.
Ask about a DAFNE course, it'll teach you about carb types & values, how fat affects carb absorption & you'll probably learn a lot about diet; most people do & it'll help you manage your diabetes better. Remember, a diabetic diet is basically a normal healthy diet: not too much fat, slow acting carbs, plenty if fruit & beg, easy on the sweet stuff. You don't need to cut out sweet things completely, just be sensible & have them with a meal when you can add the sweet carb to your mealtime injection. But the sweet stuff will always cause a bigger spike after your meal, so don't be concerned.
Managing diabetes is an art, you'll get there & discover what works for you. What I have always found is that I am not a "normal" diabetic, I seem to react to everything differently to how my doctors tell me that I should react. You'll find, on this forum, that there's many "not normal" diabetics, so many that I wonder where the doctors get their "normal" diabetics from. So don't be disheartened if you don't react exactly as you're told "most" people do!
This forum is a great place to find help & support from others like us. It'll get easier over time. Chin up :?