Irrational fears and panic

Hello all. I am new to the site. I am trying to find a way to control my irrational fears without meds. I usually have anxiety and panic attacks about once a month. The smallest idea can get in my head and my body reacts violently.
My newest problem is that I am panicking about rabies. I held a baby raccoon that is being rehabilitated a week and a half ago. Keep in mind, it did NOT bite or scratch me. The lasy taking care of it told me that it would be able to get shots at 10 weeks of age, so it had not been vaccinated yet. This is when the panic set in. Three days later, I had to go to the doctor for an allergic reaction that caused me to itch all over. (Could have been anything.) I told the doc about the animal and she assured me that without being bitten or scratched, I am fine. Since it is allergy season, I have had an excessive amount of stuffiness/drainage, but even the drainage in my throat feeds my fear.
I know I am being irrational, but no matter how much I tell myself I am fine, I still shake, have sweaty palms, tightness in my chest, heart racing, etc.
I want the panic/anxiety to stop, but I'm not sure how to go about it. I am not the type to look things up on the net since that would only put more ideas in my head and probably cause me more panic.
Any suggestions?
Thanks....

Hi, Bellatrix, welcome to PsychCentral!

You might want to read Dr. Clay Tucker-Ladd's online book, Chapter 5, see if you find something that might help?

http://www.psychologicalselfhelp.org/