I think you could do with a few pointers from a good cornet/trumpet teacher - but make sure you choose wisely. It's a good idea to ask around as it's often a better investment to pay more for one lesson with an established professional. You could also do with buying "The Good Brass Player's Guide" by John Miller - I think the ABRSM publish it. It's a great book with lots of tips on how to hold the instrument etc. and puts a high emphasis on the importance of buzzing with and without the mouthpiece (this will get the lips vibrating properly therefore improving sound quality). I think the book is only around the £8 mark and is worth it's weight in gold.