The answer to this question depends on a couple of other factors. If your medical plan is an HMO, you are discouraged from using the services of a doctor outside the plan's network. If the plan is a PPO, you can use services outside of the network at a relatively small additional cost. If you belong to a POS health plan, you are free to use any doctor you choose.
Under an HMO, you can only use doctors outside the network if you are willing to pay for those costs out of pocket. In some cases, the plan will pay a portion of the costs, but will never pay more than the same services would cost in-network. If you are prepared to pay a majority of the costs, you can use your own doctor.
Under a PPO plan, you are allowed to use the services of doctors out of network, but the plan will only pay the in-network amount to them, leaving you to pay any difference in cost. This plan will cost you less for out of network care but still carries a risk of higher expenses.
Under a POS plan, which is less than common than HMO or PPO plans, you are free to choose your own doctors regardless of whether they are in-network or not. This type of plan usually includes a base price for services regardless of where you obtain them, along with copays or coinsurance costs that you pay out of pocket. If you want to see an out of network doctor, this type of plan works best, but it still results in some out of pocket expenses.
The most affordable method for you to use is to choose a new doctor that is in-network. You may have to adjust to a different medical staff, but your costs will be minimized as compared to the other options. In any event, once your doctor leaves the network, it will cost you more to continue seeing that caregiver.