First, if your general practitioner doesn’t have even one suggestion at all, I’d suggest thinking about a new general practitioner. This is quite like saying “my leg has fallen off can you put it back on?” And your doctor saying “well I can’t and I don’t really know anyone who can. Have you tried google?” If that sounds absurd, it’s because it is. Mental health is important.
Second, if you love your GP, try asking around other people you know. Ask on Facebook or twitter or LinkedIn for your friends recommendations. Don’t be embarrassed. Mental health is important.
If you are a member of a religious or social organization, ask the leaders of that. Almost invariably religious leaders have good recommendations. They talk to a lot of people and often have a good understanding of mental health issues and who can solve them.
You can also ask your insurance. Insurance companies often have a referral service. It won’t be as personalized but it will have some help.
Now once you hit up all these groups then make a list of 5-10 therapists and call them. Have a few minutes phone conversation. See what they are like. Then make an appointment.
Whatever you do, please don’t give up on finding someone. It will help. It’s a good thing.
Taking an analogy you made, if my leg fell off, there are quite literally thousands (or tens of thousands, or hundreds of thousands) of places in the US that could legitimately help you.
The mental healthcare landscape is more like "there are thousands, but only a few you mesh with after expending a lot of effort to find them can probably, maybe help". Wtf.