Get an attorney that does specifically employment and/or medical law. You can discern their specialty focus from their website ("individual" or "employee side" employment attorney is what you want... many only rep employers/hospitals side). The medical ones will be "plaintiff" or "defendant" attorneys... sometimes not in that exact language but not hard to figure out. You want a "plaintiff" one in that case (defendant ones are largely your ambulance chasers who can't bother with small cases), but employment attorneys are usually easier to find and better for contracts.
They will usually cost 300-500 per hour.... no free consult, no discounts, usually 1 or 2hr minimum for any decent one. Well worth it. If you find one for 200 or 250 per hour that does free consults and can talk tomorrow, then keep looking. Contract review should just take an hour typically. Some might give you back the consult hour if you retain them (but you wouldn't for contract review).