$10? Damn i'm jealous Nygeel... my local gym is friggin $150 a month, which is one of the reasons I stopped going, the other was it was just too much dang effort to get into my binder just to go to the gym. So I settled for just doing weight training at home and doing my runs in my neighborhood, which still required binding but at least I was closer to home.
If I end up having the time (in between course work, riding my horse and practicing archery) I may have a go at the gym at my new university, since I don't have to bind now and feel more confident about how I look but my schedule will be the biggest judge.
In any case, good for you!!! Keep it up, they always say if you can do it for 30 days it will become routine and be set in your mind so just keep at it and soon it will just be natural to want to go to the gym at the end of the day. Sounds like you've got a good routine too. As far as your concerns with if your doing enough, you can always
a) get a trainer for a session or too, explain to them what changes you want and ask them to show you some workouts that target those areas, they will also guide you on how long and how many reps to go for
b) watch other's. If they seem friendly you can even go up to them and ask them to show you what they are doing, chances are they are just as self conscious and nervous about the gym as you may feel and will be happy to show you. If you don't have the confidence, or they don't seem like the kind of people who would appreciate you interrupting them then just watch them, what what they are doing and take note of how long they do it for, then look at their body. If they look how you want to look, try doing the exercise they were doing. Your body will let you know how much you can do, just remember to keep good posture and don't cheat during your reps.
I get that same feeling too (or did before surgery, right now I can't lift anything, grumble), you do ten reps, take a rest and then you're thinking "lets do ten more!" I've gained a good amount of muscle in my arms from doing only ten reps once of several different exercises over the past few months. Now I want to really start to gain more definition so i've up'd the reps and sets but I WAS gaining muscle. As long as you are working yourself with good posture and no pain, you will gain muscle so don't stress to much over 'how many' or 'how long'.
Again, good job!