When you first start trying to learn Celtic music you will inevitably feel like you need to play faster to keep up with everyone at the session. People tend to play fast as it gives extra energy to the music which adds to the enjoyment of playing, but some players play so fast even accomplished musicians struggle to keep up. As you learn a new instrument you will feel compelled to increase the speed you play so you can keep up in faster sessions but the more you play particular tunes the faster you will get. Don’t be scared in a session to say “Gee that was so fast I couldn’t keep up, can we go a bit slower next time?”, most musicians will happily oblige. Sometimes the speed of tunes will unintentionally increase (due to over enthusiasm), it’s more important to keep a steady beat throughout the music, a deliberate increase in tempo could be used for an extra energy lift when transitioning from one tune to another.
As you learn new tunes you will always start very slowly and once you have memorized the notes you can start to increase the speed you play. Start with very small increases in speed each time you repeat the tune (don’t speed up in the middle) and keep getting faster until you “fall off” your instrument (start making mistakes). Then have a break and come back to it later, you will find each time you try this you will get a little bit faster before making mistakes. Practice, practice, practice….