Gym training

It seems your legs and forearms are not used to be trained. If you feel sore muscles on these that's normal. When I started workout with hard ones (for example 3x10 diamond pushups or many variations for abs) I got sore muscles for a week (!).
And if you don't feel pain or sore on the muscles you train than your muscles are used to the workouts you do. Do more reps for your trained parts (chest, shoulders, biceps etc.) to get growing muscles and stamina

 

But keep in mind do not exaggerate to often, else you can take injuries (like torn ligament, inflammation in shoulders or legs etc.). If you feel pain, that differs from sore muscles, stop and take care of it.

 

are you just getting started? Wait for the results, what do you expect...

if your weights do not satisfy you try with caution to increase them a little every 2-3 weeks

 

You don't need to lift to the point you feel sore every day. DOMS (delayed onset muscle soreness, that feeling the next day after a workout where your muscles are super sore) shouldn't be your indicator of whether or not a workout was successful. You're more likely to feel it after doing a movement you haven't done in a while, or working harder at a movement that you've done before. But like Rahab said, listen to your body: if you feel actual pain instead of just soreness, that's a sign that you need to stop and not do that movement for a while. Then go and ice it and rest for a few days, and don't do any lifts that make that same place hurt. You don't want to make it worse.

For example, I can have a day of super heavy squats (doubles or triples at 90% of my max), and feel totally fine the next day. Then another time I'll do a heavy single at that same weight, but do two dropsets right after, and be sore for multiple days. Yet both times, I'm still moving the same amount of weight and I'm still improving.

Keep going man. Lifting is fun as hell.