How do I communicate with my teachers (I'm shy)?

So I've missed almost more days than I've actually attended school. I recently got a blood test and other tests are being done to where I've been "excused" (I'm sick a lot.) I feel like I've lost any kind of potential relationship with my two teachers. I am a shy girl, but I really SO badly want to approach them and speak to them both individually. I want to say "Mrs. Reid , I am really sorry for missing so much school. I had tests done and we are figuring out what's wrong, and I just want a new start. If there is any work I can make up I will finish it all. I want to make this a fresh start" I want to say that to both of my teachers, just my being shy is getting in the way. What can I do to ease myself,and is there anything I can say to put it less bluntly but still express my shame and eagerness to get back on track in school? Thanks