Hi AJB,
Welcome to the boards! And welcome to the wacky world of therapy. You sound really normal to me.
Two to three weeks between sessions seems like a long time to me but since you're just starting, your therapist may want to get to know you and any issues you're dealing with before deciding on how often you should meet. Once a week is pretty common for most "talk" therapies. Your emotions going crazy is actually a good sign. That probably means that talking in therapy and being listened to are allowing you to feel more of your emotions. Depression is often the result of pushing away our needs and emotions because either we believe they aren't important and/or won't make any difference. Not mattering would get anyone down.
The most important thing in therapy is being as open and honest as you are capable of with your therapist. This will usually grow over time as your trust in your T and the relationship grows. Its not your job to understand what's going on (although I would certainly encourage you to ask questions!) but to bring yourself, as honestly as possible into the room. Your T is the one that should be noticing patterns, and figuring out what's going on in your unconscious so they can bring it to your attention so you can make the changes you wish.
I would definitely say all this to your therapist. Tell your T you're not sure how it works and you would like more information. You can also talk about your difficulties with how far apart sessions are. Everything is good input.
The best part, though, is the fact that you've found this site. Shrinklady (site admin) has a lot of articles which explain therapy and what happens more clearly than I've ever seen it laid out. I'm one of the hard cases and have been in therapy on and off for over 20 years. I'm on my second therapist (first retired) and the information on this site has really resonated with my experiences. Shrinklady has also managed to articulate things I knew, but had no idea how to say. I really urge you to do some reading around the site. A good place to begin is
Therapy 101.
Last, but not least, we're a small but amazing community. As you read, and as you go to therapy, feel free to post questions. The people here are all in therapy and can often offer really good insight into the process and how they've dealt with similar issues.
Hope to be "seeing" you around!
Attachment Girl (aka AG)