Considering that it's the same mouthpiece you used in elementary school, mouthpieces models for beginning instrumentalists are sometimes selected on the smaller side (smaller mouth + smaller mouthpiece = better chance of success!)
There are several reasons why you should invest in a larger mouthpiece, and below are a few:
Horn mouthpieces are cheap - not like tuba mouthpieces which start at around $130 a piece.
A larger mouthpiece will be more comfortable. You've done a lot of growing since elementary school, and a larger mouthpiece will more appropriately fit the shape of your mouth - more specifically, your lip size. By having a mouthpiece that fits your mouth appropriately, you will allow your lips to buzz as necessary with a correct embouchure that will (with time) create a nice horn sound. Jamming your yappers into a small mouthpiece will not only degrade your tone quality, but it will develop bad habits and make it that much more difficult to get back into playing shape.
A larger mouthpiece will help consistency of tone quality throughout your range. The larger the mouthpiece, the more resonant and full your lower-end will be. Normally, especially in the case of low brass this can result is lost of the upper-range, but since horn mouthpieces are so small normally the change should be negligible in the upper register.
If you do decide to upgrade, here are some things to consider:
- Rim size - a large rim is more comfortable, but a smaller / sharper rim is more articulate.
- Cup size / shape - cup size and shape determine how your air is funneled into the instrument and will affect not only tone but how you project in different ranges (one of the reasons why some trumpet players love "lead" pieces.)
- Material - different mouthpiece materials feel differently - some people are allergic to nickel, some prefer stainless steel, some prefer gold / silver, and some prefer glass. There is really no difference in sound but personal comfort. I personally find stainless steel more comfortable than nickel, but I like my nickel piece more, haha.
- Shank / Bore size - this determines how much / how quickly air gets into / through your horn. The larger the bore, the less resistance and the more air is needed, but you get a deep sound. Smaller bores are good too, especially for regulating airflow on a very large horn. Neither is better than the other, it just depends on your playing needs / preferences.
- Bring your horn with you - wherever you go to check out pieces, bring your horn so you can play them and find out what you like best. If you find a model you like, try and find a better price on the internet. Don't ever buy without playing.
Best of luck.