Lots of good advice here.

You are only a month in. Stick with it, and you'll see good gains by the end of summer.

Speed vs power
Boosting an average speed by a couple of mph is no easy task.

It takes a lot more power to go just a little faster. For example, see this bike speed calculator. Taking the default settings, 85 watts gives 14 mph. It takes 138 watts to reach 17 mph. That's 60% more power to go 20% faster! And doubling the power to 170 watts only gets to 18.5 mph.

Being more aero helps somewhat. The same calculator shows 85 watts in the drops gives 15 mph.

So, realize that each small speed increase is a good milestone, and you are making progress!

Riding
Try a little of everything, and skip a day or do an easy ride after a long or hard ride. Do some longer rides, maybe 2 hours to start with, and see how you do sitting on the bike that long. More riding time is probably more helpful than more hard efforts.

On another day, try some short, fast efforts with easy pedaling in between. Even better, find some (easy to moderate) hills to climb--I have more motivation to push on hills, instead of random flat road sprinting. It's all good.

Working on a faster cadence is helpful. Try riding at one rear shift easier than you would normally do. I counted right side pedal strokes for 20 seconds and multiplied by 3, just to get an idea of what cadences I was using.

Group rides
Group rides can be good motivation to work harder than on a solo ride. The ride seems to go by quickly, and it's fun. It's my main motivation to ride every week, I have to stay in shape to keep up! And the groups know a lot of good routes.

But a lot of group rides can be intimidating or too hard for beginners. On the faster rides, most riders have been riding for years and can ride efficiently for long distances, and are good at recovering in the draft. They can put out short, hard efforts to stay with the group, and then recover quickly.

Find a more casual paced ride. Ask at bike stores, or look for local bike clubs. They may post average speeds for the ride, but note that sometimes the speeds creep up during the year as riders get more fit. And an average speed is often 3 to 4 mph slower than the typical flat road speeds of the group, since hills and stop lights will slow the average speed a lot. Contact the ride leader to see what the ride is like. These rides typically don't do any close drafting, and are a good intro for new riders.

With more fitness and group experience, the faster rides are a blast. The draft behind a half dozen riders can be a 30% savings in power to go that speed.