First off, relax; your problem is the most common one encountered by new divers. It IS solvable, partly with simply more dives. My experience is that, somewhere between 20 and 30 dives a lot of this just seems to "click" for new divers.
I can give some general hints on how to improve bouyancy control, but would probably be more "on target" if I knew a few more things about you & yoru diving:
1) What kind of water are you diving in & what temp? (assume fw, since you're from the mid west).
2) What kind of exposure protrection are you wearing?
3) How much weight are you carrying?
4) What's your height & weight? Would you characterize yourself as "skinny", "normal", or "plus-sized" ... the ratio of one/muscle/fat changes your inherent bouyancy a bit, but not nearly as much as people think.
5) How do you descend? Are you able to vent your BC & descend easily in a head-up position, or do you need to swim down to get to depth?
6) Do you need to add a couple of quick puffs of air at depth to get neutral, or in a number of long bursts?
7) When your BC is fully deflated at depth, has your buddy confirmed that it actually IS? Often times new divers have their body positioned so that the vent is below the air bubble in their BC. They assume they're vented when they aren't.
8) What brand/model of BC do you have & where are the vents?
To respond to your questions, definately NO on going deeper to resolve the issue. If you are over-weighted (most new divers are), then the problems will get worse, not better. You'll vent air, then realize you're descending way too fast, so you blast air into the BC. There's a delay in the response to this, so most new divers over-shoot, then realize they are now rizing too fast, so they vent...usually too much, and the process repeats itself. I've heard it referred to as "elevator diving." In the worst case, they end up shooting to the surface from too great a depth, risking a DCS hit.
Make sure you know where the 2 or 3 vents are on your BC and are able to reach and use them comfortably uw. If you are head down or swimming laterally, it's usually easiest to vent air from the vent at the back/bottom of your BC. If you are "head up" then the vent on your inflator hose or opposite shoulder (if you have one) makes more sense. Make sure you tilt slightly to the side to place raise the vent a bit. New divers sometimes also only raise their inflator hose a bit when venting, leaving it in a "U" shape. Since air wants to rise, the air in the BC doesn't vent much or at all. Make sure you pull the inflator hose fully upward when using it to vent. The Seaquest BC's all you to dump air simply by pulling down on the inflator hose, which obviates this problem.
Probably most importantly, did your instructor take the time to work through bouyancy issues with you prior to your ever putting on scuba? Are you able to comfortably float in a swimsuit in the shallow end of a pool, exhale fully, and lie on the bottom? If you can't, there's a chance you're holding air in your lungs, which can add 10 - 12 lbs of bouyancy. Beachdivequeen recommended some 'games' on scuba that do much the same thing.
Good luck & hang in there...don't let normal challenges sour you on the sport. That state of neutral bouyancy, once you can acheive it, is almost magical!