Yes.
Depending upon what type of allergy that you are suspecting i.e inhalant(Hay fever) or ingestants (peanuts) will depend upon what tests will be helpful.
Inhalants do well with Skin Provocation tests where the antigens of Grass Pollens or House dust Mite are injected into the arm and the reaction determined after a period of time is noted and graded according tot the reaction. Many suspected allergens can be tested at the same time.
Food allergies can be tested in this way, but are not as accurate as Food Elimination Tests.
These types of allergies evoke a blood response where levels of IgE are raised and this can be assayed in the R.A.S.T test.
Google Skin Provocation Tests and Food Elimination Tests for a more complete explanation.
http://en.wikipedia.org/wiki/RAST_test..........try this for the blood tests.
These would not be appropriate for one or perhaps two episodes of allergy symptoms, but for more persistent symptoms, all these would be available to an Allergy Clinic as pointed out by daffy.
Any further help do not hesitate to contact me, as this is a brief assessment of a complicated condition.
There is also a con tributor on AB called LazyGun whose expertise may be greater than mine here.