Question: How can I be more compassionate to myself, to stop being so self-critical?
Answer: It is actually very important to be self-critical, as it is the first step of being self-reflective for self-improvement. In this sense, it is a way to be compassionate to yourself. Ultimately, being self-critical is crucial in making enlightenment possible!
However, it is also important to be open-hearted and open-minded to hear what others might have to criticise and praise of yourself. As such criticism and praise might not be true, this is why you need to be self-critical to evaluate what they say.
Since those who criticise and praise us are not always around, again, you should be self-critical, to see yourself accurately, as you are in the moment. Doing so is alright if it motivates you to progress, problematic only if it ends as blame that discourages progress.
You can also further evaluate by comparing yourself, with others’ help if needed, to peers – not for boosting your ego, but to see if you are doing well enough. Not that doing better means you should no longer be self-critical, but that you were too negatively self-critical?
At the same time, it is good to remember that the Buddha is our role model, that we have way to advance spiritually to be the kindest and wisest possible. The point is to keep advancing, at a reasonable and sustainable pace. If you keep blaming yourself for being slow, this further slows you down!