Kindly ensure you do a proper warm up before you start any form of exercise to avoid injuring yourself.
Having said that it's a possibility that your muscles are not developed enough to do push up and chest press with dumb bells.
Try using lighter weight dumb bell or taking rest between each set of repetition.
Hope you end your work out with a proper cool down exercise and post work out meal.
Wear a proper groin support brace during work out.
Next Steps
You have to take a proper pre work out meal which should be a combination of carbohydrate and protein. If you eat too light or too heavy or if the gap between the meal and workout is not proper then it might affect your productivity during work out.
Health Tips
For a detailed management kindly contact me online via practice consult.