Hi Nicole! :) The best thing to do is to find the right teacher that will make you feel comfortable. If it's with a woman, then filter through the females who teach. If that's not an issue, start browsing and just see who seems to have the right style and personality. Note: most Professional Teachers have likely been trained on how to help people of all learning styles. You may want to begin with a PT first.
Next, when you book a lesson, opt for a trial lesson or a shorter block of time time (usually it's 30 minutes, rather than a full hour). Send the instructor a message, and be honest about your situation. Tell them you have some nervousness about speaking to a stranger, or speaking to a stranger in another language. This way they know how to approach you. If you have any restrictions or limits, let them know.
Like everyone has said here, we've all felt a little nervous going in to our first lesson. I can't imagine how this must be for someone who suffers from anxiety. Likely, if you've found ways to cope with certain other things in life despite your anxiety, you will be able to do this too. Try to look at it this way: your trainer is like a living text book and you're here for the languages. They've likely seen it all! :)
I hope you find the right instructor and have fun improving your target language with them! Good luck!