I'm so sorry about your dad.
What you have described of your boyfriend is not normal. It is not acceptable.
I was put through this too. It stopped me from being able to grieve properly and I'm now years and years later only just starting to process it.
I also got told it was "unfair" of me to try to talk to him about it and that I wasn't allowed to anymore. After 6 months he "lost his temper" and informed me I should be over it already.
These are huge red flags. Please learn from my mistakes - this is a sign of things to come.
I understand you love him, but he is demonstrating through his behaviour that he does not love you back.
Lots of people feel uncomfortable supporting others through bereavement and grief, but this is not that. This is deliberately cruel and hurtful. He is not even attempting to support you because he places no value on your needs. Or you.
You deserve so much better than this unpleasant man. I know it must feel frightening to consider breaking up with him when you've just lost someone so close to you, but honestly this man is only making your grief harder to bear and it will take you longer to process if he continues treating you like this.
You are right, how you're feeling and responding is natural. The rawness of your pain will gradually subside, but it will continue to rise to the surface unexpectedly throughout your life. Because there is a part of your dad you will be carrying around with you.
You still have all the experiences you shared with him, and the way he shaped the person you are today. In that sense, he will always be with you, as part of your present not just the past.
As to the "get professional help" comment, generally you would not be accepted for grief counselling until at least 12 months after the bereavement. This is because grieving is a long process, it doesn't finish as soon as the funeral has happened as some people seem to expect (or in this case, demand). Although of course if you feel it would help you could still talk to your GP, or talk to the samaritans, etc.
And Token that is your issue, and I'm startled you think it appropriate to describe the pain of grief as "neediness". Humans are social creatures, we all need connection, especially when in pain or suffering. I really hope when it's your turn to experience this you do not find anybody around you telling you to hide your pain from them because it's too uncomfortable. Grief is the greatest discomfort there is.
Grief is an all consuming pain, not something that only strikes at occasional intervals so as not to inconvenience other people with your sadness. That might be how it's portrayed in the media, but it is not the reality. It's also not "negativity" to speak about the difficulties in our lives, it's reality. It's not healthy to try and suppress all of our "negative" experiences and emotions. Sooner or later they will explode out of us if we do that.
Life is not a Disney film. It is dysfunctional to coerce other people into suppressing their pain because you don't have the skills to cope with seeing how harsh the world can be for some of us.
The people who love you will be there for you when you lose someone, because they know that no matter how hard it is for them, it's unimaginably worse for you.