yep. Thats how muscles develop

I would take an "active recovery" day...such as light stretches or floor exercises to give your muscles some recovery.

If this occurs again, take a hot bath. The heat will calm your muscles. They're sore because they are over worked. The heat from a bath... simply to soak, will calm your muscles. In the future ask a trainer about your pain and the discomfort. THAT is what they are there for.
I was tall for my age growing up. And I was plagued with brutal leg cramps. I remember waking up crying. Growing Pains my mother called them. Even today I sometimes feel the leg muscles cramp up. But I do not attend a GYM I walk. Live in a very pleasant community.
I eat more or less what I want, then walk off the calories.
I could consider to jog off the calories, Was fat once. Nearing obesity. When I tried on a pair of Jeans that read size 22 I began to treat my body a lot better. Fluids. Drink as much water as you think you can hold. TRY to make sure you drink a lot of water. This will replenish what you lost AND restore what your body needs.
However, to truly answer your question...you are not giving your body the time to adjust.

Give it some time to heal. Then you will be able to do more next time. You will get stronger

I wouldn't.

I have been trying to because I tend to give up if I let the aches really set in. Much easier to sit watching The Crystal Maze and eating cookies because I'm a little bit sore.

Bananas if you can. Soreness happens due to lactic acid buildup in the muscles; potassium, and stretching, along with adjustment to the workout will help.

To lessen the chances of leg cramps try stretching before and after a workout. And drink plenty of water or Gatorade. Your muscles lose water and electrolytes during a workout.

Have a few beers at the pub. That should relieve some pain.

Take some time off, I have pulled muscles before and the only thing you do is aggravate it if you don't let it rest.