In reply to SharonC1604: Falling on lead is going to happen sooner or later, whether it is muscle failure or simply the rock breaking under your fingers. If falling off is a major worry for you (and frankly it is for most people!) then you might do worse than try taking some lead falls on protection that a more experienced friend has first inspected to make sure it is bomber. Look for places where you can take a clean fall obviously.
Making yourself more confident on the lead when trad climbing is a pretty difficult process and I don't think anyone has a shortcut (unless brain surgery of the destructive variety is included). If your fear stems from not knowing what a fall has in store for you (you seemed a little suprised that your gear held your fall) then a couple of things you might try are:
1) Get to know what gear placements are good and what are not. Practice placing loads of gear at the bottom of the cliff and ask someone which bits are good, which ok and which useless. Get someone to give you feedback on gear after every climb you lead.
2) When leading, reassure yourself by looking back at (or just remembering) the last gear, telling yourself that it is good and you know it is good and it is quite close and any fall would be clean and so you can go on to the next move without fear.
3) When you don't think a fall would be safe, get used to making a judgement call based on how the ground ahead looks, how hard a grade the route gets, any guidebook information you have and what the rock quality is like. If you think there is much of a chance you will fall, then retreat - an injury could set you back months or more and it's just another climb you are on after all.
4) Don't be afraid to put in more gear, stand ages at a good rest or downclimb to a rest/more gear. When you are on a single pitch crag and trying routes that are hard for you time is not important, your belayer should be prepared to be patient (longest I've held the rope for on one pitch is 3 hours and that isn't uncommon
5) Try seconding some harder climbs. You might find that when you feel "safe" on a toprope you can climb a lot harder than you thought and this in turn might make you more confident to get on climbs near your limit.
Ok, I'm half way through my bottle of wine so I'm going to stop rambling.