My sincere condolences on your loss. I know a bit what it might be like, as I lost my partner of 40 years in the middle of October. It has gotten better a bit at a time since, but I have had a therapist for several years that has been working with me, along with my primary care physician. And, I’ve got a strong support network (some of which I didn’t know I had until it was needed). All of those factors are helping, along with time.
Do take up your dad’s offer for the grief counseling. Look to see if there are any group offerings, too. Check in with family and friends. Stay connected. I know it is hard to start with, but it does help.
Wishing you all my best.