Welcome and thanks for your question!
Sorry to hear about your tax situation.
Unfortunately you cannot pursue both at the same time for a same liability. An offer in compromise assumes that you agree to the tax owed but have concerns about your ability to pay the debt.
An appeal is appropriate if you do not agree with the amount assessed by the IRS.
That being said, there is nothing precluding you from pursuing an offer in compromise after the appeal process is concluded.