The answer is
yes certain type of protein according to dairy industry like here (marketing whey for all kind of things such as weight loss, surely-better-than-soft-drinks -style argumenting, feels a bit strawman) but if you get enough things already from your nutrition, probably not. Be on the safe side though some extra protein such as whey straight after running is surely not bad, some fuzzy question here.
0. Calculations and Profile analysis
With 90kg, it is apparently around 135g:
but but -- is this over-estimate in your situation? Researching.
If you think that two fitness-spoons is about 30g so some protein probably not bad, depending ofc on your diet and intensity of your exercise (HF does not tell everything, EPOC more, there are services such as Movecount to monitor this kind of things). Now other type of proteins such as egg and soy. Egg weights about 50g and has about 12% protein, source. In soy about 52% of content. In whey about 76% or even more of content. And also take into account your other intake during day, can you get protein already from your nutrition?
1. Focus on general picture not on one type of thing such as protein or vitamin
Only one type of thing such as protein or calcium is not necessary. It is necessary that you get the all necessary ingredients to get long chain reactions in your body working. The reason why the next study focuses on both Ca and D2 is that absorption requires them, not just one. The quote from this study about the elderly women here:
"Combined calcium and vitamin D2 supplementation increases cortical bone density.".
There are also other things such as C that may affect things -- so at that age just take some easy to get multivitamin without confusing your head too much with technical details or rationing, even the term
"vitamin" is a pain of history!
2. Eat good quality of protein with variety
The other answer with the generalization
"Protein always helps with recovery." is wrong and misleading. The sentence is satisfied even with gelatin, not including all necessary amino acids. Again the key is
"variety". If somethnig feels bad, stop. Mix between egg, soy, whey and milk.
...anyway keep things fun -- but not too fun to lose discipline :)
Perhaps Interesting Things to Readers
Effect of protein intake on muscle recovery