Hi Cat,
From reading your description of your comfort in the water I have no doubt that you can become a fine diver. I am also hearing that you are doing this for yourself so you can enjoy something in common with your BF. It very important that you are doing this for you. The fact that you came here seeking support speaks to you wanting to make this happen. This is all good stuff and before I go on let me say that the effort will be worthwhile, trust me.
Diving is an adaptation. As a water person you know better than to inhale with your face in the water, throw that one out the window as a diver! You are accustomed to being in "swimmers" which I assume is a local term for swimsuit. Getting into a wetsuit irrespective of fit is something that many people find a bit weird the first few times. As you have learned you cannot see without an air space in front of your eyes so we wear a mask. All of our faces are different so mask fit is a very personal thing that sometimes is like kissing a few frogs before meeting your prince. Your realization that it may have been too tight could solve your leaking and some of your general discomfort.
Why were you hot? Wetsuit, pool temperature, having a cold, stress, trying something new in some combination are probably at the root. Let it suffice to say that diving will be a very comfortable sport and being hot while in the water is not a concern.
My wife and I certified together and her experience was somewhat like yours. Even with 60+ wet suited cold water skin-dives under her belt before class she found all of the gear and breathing underwater overwhelming. She had a prince of an instructor who backed off and gave her space to get comfortable with the basics before the skills. By the end of the first night she walked down into the deep end of the pool. On night 2 she was swimming with me underwater and went home knowing that this was something she could do and still wanted to do. Two more evenings had the skills down pat. We then jumped in with the next class to spend a few sessions just drilling each other as a buddy pair. Our check-out dives were a breeze.
Everyones learning experience is unique and it is sometimes a surprise to see where the challenges lie. Give yourself the time and patience to get comfortable with this. It sounds like you have an ally in the instructor (candidate) who worked with you.
I would suggest getting into the pool without the BC, Cylinder and regulator and start with some skin-diving to the pool bottom. This will get you some confidence in oral breathing, mask fit, equalization, being clad in rubber and all those new sensations. Wear enough weight to float safely but to dive to the pool bottom on a breath hold at will. A good program will begin with these basics.
When you are good with the skindiving aspect strap on the BC and slip below the surface in the shallow end and get accustomed to the regulator response, the sound of the exhaust and so forth. From there you should quickly get comfortable enough to begin your skills work.
DO NOT let yourself move on to your open water checkout dives until you are comfortable doing your skills in confined (pool) water.
Don't fret the weight belt feeling. You will grow accustomed to that. Also as a new student there is a good chance you were overweighted just to help you get down. You should learn how to determine and adjust your weighting as you grow more comfortable in the water. You will also learn that all of your weight need not be concentrated on your belt and when you distribute it for balance (trim) you won't even know it's there.
The same can be said for the rest of the gear. It can be overwhelming at first. Familiarity and some smart choices when you invest can make this a non issue.
Another important thing is to have a mask that will not fog and in case you were bothered by this
here is some information. Be sure to see the cleaning segment.
You can do this, we are all pulling for you and are looking forward to a full report after session 2.
Pete