To determine whether it's feasible to appeal a conviction after pleading guilty depends on a variety of factors. Below is a brief explanation of your options.
Withdrawing your plea
Good cause is required when you intend to withdraw a guilty plea. Simply being discontented with the situation is insufficient. If this is your intent, you must file a motion to withdraw the guilty plea and explain why this should be allowed.
Good cause may be applicable if you weren't informed of your Constitutional rights, failed to understand the charges you faced and whether you have a factual basis for the withdrawal.
Your attorney must file your Motion to Vacate your plea immediately, as you may have as few as 10 days to file after sentencing. If that time lapses, you have but one final option.
Writs of Habeas Corpus
This is the Hail Mary legal option. Writs of habeas corpus can be effective once the deadlines have passed to file a Motion to Vacate and/or your judge doesn't allow you to withdraw your plea.
At this point you must make the case for why you should be able to withdraw your plea. Maybe you entered a guilty plea to a hit and run where your best friend was actually behind the wheel. You knew he had a baby on the way and two kids at home and thought you could help him out. You later realize this was wrong and that actual video evidence exists from traffic cameras that shows you as the passenger and him as the driver. While this is just a hypothetical situation, and all cases are different, it could possibly work out for you.
It should be emphasized that you should seek legal guidance in order to present the best possible case before the court. You don't have to have an attorney to file an appeal, but it's a good idea to at least consult one.
Source: FindLaw, "Appealing a Conviction After Pleading Guilty," accessed Dec. 29, 2017