First time with personal trainer

No, you can definitely give your body some time to rest and recover. Get plenty of water and eat some protein. You'll probably feel less sore as your workouts with your trainer continue, but for now there is no need to overdo it. When my legs are dead from "leg day", I usually just take a long walk or do some yoga and call that my "active rest day"

I would recommend active recovery...something light like walking. It might help you feelbetter, although doesn't feel like it at first.

go for a walk. if you're new to all of this, pace yourself...you certainly you don't need to go from couch to all of the workouts overnight. rest/recovery days should also be programmed into your fitness regimen...it's just as important to your fitness and overall health and wellbeing as the work itself.

the worse thing you could do though is nothing...get up an moving, just nothing to strenuous.

Walk on the treadmill after a leg day, at a reasonable pace. Along with good stretching. I recommend you rest 48 hours before working the same muscle group.

The first time I worked out with a trainer, I felt like I'd been hit by a truck for a week.

I keep telling my coach he is trying to kill me or get me to pull off the impossible. He just laughs at me.

But in all seriousness, get some gentle movement in. A long slow walk will do wonders.

No I would just walk. You are tearing your muscles when you workout and the rest time is when you grow and repair. You will be stronger for the next workout. Don't overdo it or you may find that your immune system is a little weakened and end up getting sick. Your body will adapt to the workouts in the first couple a weeks and you won't be so sore after that. Your trainer should be able to tell you how much you should be working out and when. Don't be afraid to ask them. You are a paying customer. Ask them lots of questions. They are usually very expensive. Get your money's worth from it.