I am so sorry that you had to find out the truth this way, it's a cruel thing to do to a child - hide the truth about your identity and let strangers reveal it maliciously to you. Parents sometimes make these decisions (to keep a secret) thinking they are protecting their children. However, usually it backfires. Unfortunately, because of who your daddy was, this backfire has been made public and the entire world is watching you. It's not fair, but make the best out of a bad situation.
But don't feel alone. There are thousands (maybe millions) of kids out there just like you - conceived artificially and denied the right to EVER know who their biological parents are. You three can change this!! Stories are flying around that your dad's dermatologist is your biological father. If this is true, you deserve to know, to know him - as your father. Ask questions, demand answers! Not only can you find answers for yourself, you can help thousands of other kids and adults out there who were conceived the same way!
Your daddy will always be your daddy, nobody can take that away - and it will take time to mourn his passing. But you also have a biological father out there, and you carry half his genes. His is part of you - he even looks like you! While nothing can mask the loss of your daddy, I hope that your biological father will step up and give you guidance and love, and support through this rough time and as you grow up. You deserve that as children and as human beings.
You also deserve to know your biological mother, and I hope for your sake that she stands up and acknowledges herself to you and provides love and support. A child needs both a mom and a dad, and to have only one and lose him is tragic but to be denied the ability to know both biological parents is horrific.
If you ever come across this, in a few weeks, a few months, even a few years - please know that you're not alone and that there are many others out there pleading for these same rights...and that one day we will prevail.