It is natural to feel withdrawal symptoms like anxiety, shaky hands, headache, nausea, insomnia, and sweating when alcohol is given up.
But it all depends on -
1) how long you've been drinking for (months, or years) is it habitual.
2) how regularly you've been drinking (how many times in a week)
3) how much intake of alcohol do you take every time.
If all of these criteria are a little more than normal intake then it is natural too feel withdrawal symptoms when you leave or abstain from alcohol.
Next Steps
The only solution is to patiently deal with the symptoms.
Increases heart rate & Anxiety
These two symptoms usually co-occur and practicing breathing relaxation exercises will help. (google and practice box breathing). The idea is to calm down your body and mind. This will also help in getting a good and sound sleep.
Eating healthy and staying hydrated are very important steps to help your body get good amount of nutrition to deal with the withdrawal symptoms.
Health Tips
If the symptoms persist. And if you were a regular, heavy drinker then it is best to meet a doctor who can help you easily adapt to these changes. And check if there is no physical damage to the body due to long term alcohol use.
Meeting a Psychologist will also help, if you are unable to control yourself from staying away from alcohol. They will help you prevent relapse.