The answer is yes

"Because you are being tested, it is expected that you will make some mistakes. I assume that you have done things in your life that you regret, things that you cannot even apologize for, much less correct; therefore, you carry a burden. You, perhaps, may feel inferior in mind and body and are troubled or burdened with the weight of some spiritual account that is marked 'past due.'

Too frequently we receive letters from those who have made tragic mistakes and are burdened. They beg: 'Can I ever be forgiven? Can I ever change?' The answer is yes!"    
Boyd K. Packer

Are we not all beggars?" Don't we all cry out for help and hope and answers to prayers? Don't we all beg for forgiveness for mistakes we have made and troubles we have caused? Don't we all implore that grace will compensate for our weaknesses, that mercy will triumph over justice at least in our case? 

Jeffrey R Holland 

"None of us will be on earth very long. We shouldn't wait to be happy until we reach some future point, only to discover that happiness was already available—all the time!"  
Dieter F. Uchtdorf

"Christmas is a time for remembering the Son of God and renewing our determination to take up on His name."
Dieter F. Uchtdorf