A general support group may be less threatening because it does not specify any one type of grief. You can always choose how much you share and when you are ready to share it. Initially you can keep the more personal issues you are not comfortable sharing, to yourself. That is totally okay. Wait until you feel safe to share. This is a process.
I would always do my homework and make sure the group leader has some experience and even better, is credentialed. A good counselor guides the discussion and offers encouragement. The leader and the participants share strategies for coping that have worked for them.
Coping with the loss of a child is tough. You may need a group that can handle the specifics of this kind of loss. It helps to be with people who have experienced a similar tragic event particularly if members of the group are further down the road of grief recovery than you are. They can give strategies and support better than those that have not experienced this kind of grief. Grief can sometimes lead a sufferer to feel as though no one else understands his or her pain; a specific grief support group can help eliminate this feeling of isolation.
Don’t forget there are online support groups. If this is the best you can do, then start here. Personal contact is best but get your support from where you are comfortable. If face to face meetings are difficult, an online support group is a good start. This can be a first step to attending an actual face to face meeting.
Making that first step is the toughest. If you need support, ask a friend to go with you to your first meeting.