Post workout effect. Is this normal?

I was working out yesterday, 10 mins tread mill, 10mins cycling, 30 crunches, 40 squats, bicep exercise 3 sets(5. Rep each with increasing weight)., 2 mins plank. After workout i was sweating a lot, i drank enough water too. But after some time, i felt current like in my arms and my palm/fingers were getting tight and closed. I felt a little dizzy also. Then my trainer came and poured cold water on my arms, stretched a little and i had to keep my arm under normal water for sometime after that. Then it became normal. So is that happened because I overdid the exercise. I used to go to gym few years back, never experienced such. This time I started and this happened on the 4th day(maybe bec i worked out more). Also after getting normal i ws still feeling dizzy and my mouth was dry until i drank mausambi juice. Is this normal? Please let me know why this happened so that I can avoid this in future. I felt a very very very slight pain at the back of my head too.