Why do you need to convince your uncle of anything? This is bothering you significantly. What bothers other people or not isn't the relevant issue. I don't know if going to the hospital is needed or best for you - that depends on your level of safety right now or symptoms that could potentially be treated better in the hospital. Guilt and shame can be very intense, but these are emotions everyone experiences. It helps to have support working through them when they are very strong feelings. Talking to a therapist or to a clergy member can really help. You are 27. You don't need anybody's permission.

You know your uncle's position, and you know your other family members' positions on this issue. You chose to talk to your uncle for a reason, and got his answer. You chose him because he wouldn't freak out and make a big deal and add to your shame and guilt. It sounds like he tried to give you the support you asked him for. If it was not what you needed, what do you need and who would be able to give that to you?