Why would you be so hesitant/resistant to going through your own services exposure report process???
If on the tiny chance you actually do catch something, there's so many advantages....besides that your service pays for it, if you had reported it to your Supervisor (or whoever you're supposed to per your services policy) immediately after the call, they'd pull you out of service and send you to the clinic, but you're still on shift so not only are you not having to pay to be tested, but you're also getting paid to go get tested.
Then IF it is positive for whatever, wouldn't that be workers comp? Or otherwise covered by your services insurance, be put on light duty if need be, etc etc.
Vs if you just go yourself? Besides paying out of pocket, IF it is positive, what then? Hope your health insurance is good enough to cover whatever treatment? Hope your deductible isn't $500 or you're still paying that much out of pocket for everything, that can add up real fast....and oh yeah, if you now can't work in the field, just hope your service is willing to just take you off the schedule for an office or dispatch spot...what if they don't have any available, or if they do, what about returning to the field? Would you have to reapply from scratch?
There's all sorts of liability and no benefits to doing it yourself if you are worried about potentially catching something. If you haven't already, call whoever you need to to activate the exposure report process NOW. Otherwise you are quite literally on your own...