What makes you think it was the 11yo and not the babysitter? Did the 11yo have a friend over? What other problems make you think it is the 11yo?
Do NOT ask the 2yo questions. Call children's services and have them do a forensic interview (designed to figure out what, if anything, has happened with-o leading the child). Usually it will be done with very little wait. If they find abuse they will have ways to help you.
This is NOT something you can handle alone. You NEED the professionals, and either the pediatrician or you need to call and report this. It is a good idea to take your 2yo to the pediatrician to ask for help. This will mean the doctor has to make a report to CPS, but they will say that you came to them asking for the doctor to make it and to help you. That is a good thing.
Are you and the 2 children the only members of the household? One thing that CPS is very likely to say is that an 11yo is too young to be left in charge of a 2yo for any length of time. In some areas you cannot leave an 11yo home alone by themselves, but the laws on this vary widely from area to area. As a general rule most places that give an age for the youngest you can be to babysit use 13 or 14yo. Even if this is the case, they will just let you know so you don't let the 11yo babysit again (as if you would after this).
You also need to take a good hard look at anyone else in your life that could have hurt your child. If it is your 11yo, she needs a LOT of help but you are going to have a really hard time finding that help. We don't really have services that know how to handle a child who is sexually abusing another child. So you will have to do a lot of searching and trial and error.
I am so sorry that your 2yo was hurt this way, and that you are going through the added agony of suspecting your older daughter of hurting the baby.
In the meantime, work out a written safety plan to protect both children. This means not leaving them alone together and making sure that they don't contact each other at night while you are sleeping.