Yes. But, it’s better if you say nothing about your prayers and just pray.
I get it, we want to feel like we are supporting those who are suffering and contributing to some good after something horrible.
[Mat 6:1, 5-6 ESV] 1 “Beware of practicing your righteousness before other people in order to be seen by them, for then you will have no reward from your Father who is in heaven. … 5 “And when you pray, you must not be like the hypocrites. For they love to stand and pray in the synagogues and at the street corners, that they may be seen by others. Truly, I say to you, they have received their reward. 6 But when you pray, go into your room and shut the door and pray to your Father who is in secret. And your Father who sees in secret will reward you.
Generally, our prayers should be a secret thing, as our giving should be as well. The main point is not to be a hypocrite.
But, when expressing support to others who are suffering saying “my thoughts and prayers are with you” has become often times just a saying.
I don’t think you can’t say it. Just say it in a way that doesn’t sound cliche if you do. More important than saying it, though, is doing it. And the way we are supposed to do it is in secret.
Even more important is to not let people’s frustration with the saying stop you from praying, or stop you from expressing comfort and support for those who are suffering.
Just find ways to make your support sound more sincere.
Shall Speak To Nations 
I have found shock and gratitude when I inform others that are going through trials, tribulations, and sorrows that they are in my morning prayers and am there for them if they need me (it is said with conviction, do not say it if you do not mean it).
I think that’s a good thing. I think the issue I’m getting at is that there is some truth to the criticism of people over using the phrase without thinking much of it. I’m mostly weighing in on the social media trend. Which isn’t bad, but maybe could be done better. Either way thank you for commenting and sharing!