The Yamaha 4C is a basic mouthpiece that should serve you well for now. If you are in your first year of playing, I would not advise you to go on a quest for the perfect mouthpiece just yet. I have to echo John's advice of a #2 ½ reed with a slightly larger mouthpiece, though for right now, yours is fine. The Yamaha 4C's tip opening is quite small, around .063" for the alto. In the near future, you would perhaps be better served with a comparable model with a tip opening of .066"-.070". For a beginning alto saxophonist, the Bundy #4 is excellent. The student on a tight budget will find a great bargain in the Woodwind & Brasswinds's Bundy "Special Plastic" model. For tenor sax, the Bundy 3 or 4, or other good student mouthpiece in the .074"-.080" range is a good choice. There is no need to buy a higher priced professional quality classical mouthpiece now. The student models are specially designed for your playing needs.
It might interest you to know that most pros play with #2 ½--#3 reeds (but with larger tip openings on their mouthpieces). Reeds... when in doubt, throw them out. This is not the place to be frugal. Buy reeds by the box, or at least 4 or 5 at a time. If you are not buying at least 4 reeds a month, for school playing, you are suffering.
You have a very good saxophone (Yamaha-52 series) that is capable of professional playing. Even though your sax is only two years old it may still have a leak. A small cork can fall off and a pad may not close fully. Any number of things can cause a leak, not just aged pads. Even new saxes suffer from leaks and maladjustment. This is no one's fault or shoddy workmanship. Pads and corks continue to settle in, compress for a period of time after first being installed (many repairmen use techniques to help reduce these problems). So, please take it back to the shop and have it inspected, "leak lighted", and adjusted if necessary. Also, have a known good player test the sax.
More than likely it is an embouchure problem. Playing with too much pressure is as bad as too little. There is a "just right" amount of pressure that will allow you to play the full range of the sax, with fairly good intonation. There will be a few notes that need to be lipped in tune, but generally, you do not need to be making drastic embouchure changes. It is NOT proper to drop the jaw or loosen for low notes, or to tighten for high notes.
When a young player has difficulty with playing high notes, it may be suggested by a teacher, another player, or through experimentation that a tighter embouchure may help. Conversely, it may be suggested to use a looser embouchure when there is difficulty making low notes respond. Then the player makes the wrong assumption that it is always necessary to tighten for high notes, and loosen for low notes. If you can play the low register, but have trouble with the high, you are also too loose for the low register. If you can play the high register, but not the low, you are too tight for the high register, too. So, how do you find the correct amount of pressure?
Well, first let's form the correct embouchure. This simple method was taught to me by a fine player who is now an instructor of clarinet and sax at the US Armed Forces School of Music... are those credentials enough? Now, this is so simple you will think it can't be right...
Now, this is his method...
Can you suck your thumb? Of course you can! Put your thumb in your mouth (about ¾") with the pad of the thumb touching your top teeth just as the mouthpiece does. With about half of your bottom lip folded back over your lower teeth (this is subjective, less lip if your lips are fat like mine, more if you have thin lips), simply suck your thumb. Now, notice that the chin is flat the cheeks are not puffed, the lips are drawn around the thumb in a circular pattern... like a rubber band. For the saxophone, simply blow instead of suck. The rest is the same. Simple? You bet! That is all there is to it.
Next... you need to know how loose or tight to make the embouchure. For a more thorough explanation, read my Sax on the Web article, Tone Production for Beginning Saxophonists. I would like you to do this using a piano or some other source of the note A = 880 Hz. This is the A one octave and 6 steps above middle C on the piano. Play the A, and match this pitch while blowing only the alto sax mouthpiece (or G one step down for tenor sax). That's right, no saxophone, just the mouthpiece. Play a good, strong tone, with lots of air. Do this for 5 minutes a day as the first part of each practice session. Then, when you put the mouthpiece back on the saxophone, play with the same embouchure tension. In a week you should be able to see substantial improvement in your tone and intonation.