Oh OP, I am so sorry. I had the same thing happen with my first baby. I remember those first few weeks of shock and grief and fear, and physical and hormonal upheaval.
Sending you lots of love.
It is fine to skip your 6 week check - but ring ahead and let them know, or have someone do this for you if you can’t bear to have that conversation yourself (I know I couldn’t have). The last thing you need is a cheerful receptionist calling to remind you, or getting a visit from a child safeguarding team if you don’t show.
If you do decide to go, be prepared to explain to the receptionist that you do not have a baby with you to be checked as well, as that is what they’ll be expecting, since maternity services and GP services don’t communicate at all, and you can’t count on anyone having looked at your patient notes.
Also, go in with a clear aim in mind of what you want from your GP. What do you need checked? What do you want referrals for? Mental health support? Physio? Follow up for birth injuries or blood loss?
It’s easy to fall into the attitude (sadly encouraged by many medics and midwives) that your own postpartum body doesn’t matter, in the absence of your baby. But you are here, and you are the patient, and your health is important, and your comfort matters.
Hang in there. It is so so painful. And you’re not alone.