To run faster you need to run shorter distances. To run further you need to run slower.
Most people do one long run a week. This is your long slow run. The longest run of the week. You need to keep the pace slow and comfortable. This run will help build your endurance.
As a beginner don't worry about trying to do speed work like Fartlek or Tempo runs or intervals.
Just do one short run each week where you are pushing the pace. You'll need to warm up before you get going at the faster pace. Even if all you run is a mile at the faster pace to start with it's a beginning. You may want to aim to get up to about 3 or 4 miles though. Don't try to maintain this faster pace any longer or you'll wear yourself out which will invite injury.
Short fast runs are actually quite good fun esp if you have somewhere nice to run.
These 2 runs will help you. If you can do at least one more run, 2 would be better at a slow pace. Mix it up, go off road, include some hills, go somewhere fun.
I run with a club and I know I'm very selfish. I'm one of those runners at the front always trying to push the pace. I'm probably far more annoying than you are. I do compete with the other front runners, trying to keep up or run faster. It's how you improve.
So, don't stop running with the club, try and keep up with the others, it will hurt, don't worry about that. You'll make progress even if you can only cope with one run every 2 weeks to recover.