Is it normal for me to feel sick when I work out????

So I'm not a very active person when it comes to working out especially after a year of not going to the gym due to the pandemic. I would just occasionally go out for a jog around my college campus. 

The gym at my student housing opened back up and I've been going for two weeks now. I first began slowly and everything was fine for the first week. The second I started to add more workouts like at least 15 to 25 minutes of cardio depending on my mood because. hate cardio,  4 sets of 25 of chest workout, 4 sets of 30 of ab work outs, and 4 sets of 20 of arms. (I know it isnt a lot but im a beginner and not used to working out as much)

for two weeks that i have been going have been fine and been feeling good even after i got my first dose of the covid vaccine 3 weeks ago. 

this week went 3 times, monday, tuesday and today i skipped yesterday and almost today due to not feeling well. (Been feeling anxious and depressed been going through a lot of stress atm) 

anyways after i finished working out today i started to feel nauseous to the point that i want to puke while im working out...and after I finish working out the feeling still lingers. 

im only allowed to be in the gym for an hour so i try to do 45 minutes of a complete workout and finish off with something light but m usually there for 45 minutes. today i only lasted 30 minutes.

did i just overwork myself that caused me to feel ill?