Can you have an allergic reaction to a tick bite?

Yes. Yes, but not an anaphylactic reaction to the tick bite. Usually it is only an itchy local reaction. This is a sign that you are developing an allergy to a component of the tick saliva. It is common for the bite site to itch for several months. It is not a sign of infection. This can set you up to develop other allergies. For more information check out the "healthguide" " delayed meat allergy...".
Yes. Technically yes, but people who have an allergy to a tick bite are likely sensitive to any bites, i.e. Mosquito, sand fly, etc. Topical anti-inflammatory creams/ointments can help decrease any swelling or redness. It's important to recognize that deer ticks can carry the pathogen for lyme disease. If you're concerned about a deer tick bite, I would discuss your concerns with a physician.