Hi Huba, really sorry for your loss. I may not understand exactly how you feel but I can relate to your current circumstance. I lost my dad about 10 years ago now and it was a really hard blow for me. My dad was my best friend and we were really very close. Not having the time to say goodbye and all that happened prior to his death really had me shattered. However, I thought I had to act strong and not show how I felt and I did that. Honestly, it did me more harm than good. I grew numb because of it and I was at an empty place emotionally. Looking back I wish I allowed myself to grieve.
The truth is you've lost someone really dear to you and it hurts. I think it's okay for you to grieve and cry and take a break from everything. You need to give yourself permission to though. Grieving is how you can move forward and not let this hold you back from living. Take some time, write out how you feel, talk about it, sit and cry, just do what you want to.
Shame is a terrible emotion and I have come to find that when we actually open up and be vulnerable about what it is we feel, we find the courage to move on and deal with it and more often than not we find an army of people just waiting to embrace us and walk the journey with us. Please don't feel ashamed, there is nothing to be ashamed of. Feeling sad doesn't make you weak, it simply means that you are human with emotions and while how every one of us process these emotions will differ it doesn't make any way better than the other.
I'm sure your dad would want to see you live your life and live it to the full. Please give yourself room to grieve your loss. It's completely okay to need others to carry you for a while or not have it all together. My thoughts and prayers with you and I pray that you will find the strength and freedom you need to grieve and the comfort, healing and hope to carry on.