I cannot remember who the quote is from but I've heard it expressed this way as well.
Grief is love that has nowhere to go.
Edit: Found it. Here's the full quote.
Grief, I’ve learned, is really just love. It’s all the love you want to give, but cannot. All that unspent love gathers up in the corners of your eyes, the lump in your throat, and in that hollow part of your chest. Grief is just love with no place to go.― Jamie Anderson
I cannot remember who the quote is from but I've heard it expressed this way as well.
Edit: Found it. Here's the full quote.