An elevated IgE is not significant unless there are associated symptoms to account for the elevated count. Yes you can take the Covid vaccine as long as you don't have a severe allergy (anaphylaxis) to any of its ingredients. some people can have IgE values more than 3000 - 4000 and not manifest many allergic symptoms.
Next Steps
if you don't have any known allergy, register for the vaccine and mention to the vaccinator about your allergies before having the injection. they may have to monitor you for longer or take other precautions.