Note that blood and pus are considered as najis (ritually unclean)by most scholars (See for example What items are considered najis in fiqh?). Ibn Taymiyyah is among those few who considered at least pus as tahir (ritually clean). So praying with one or both of them on the body or clothes may make a prayer invalid.
Nevertheless as it is the case with water a large amount of tahir/clean material wipes away a small amount of najassa (unclean material) scholars had different opinions on the amount or dimension that limits what is considered as small amount of blood or pus:
As for the hanafis they said it is an amount that is equal or smaller than a Dirham (a known measurement/coin), the malikis considered what is below the dimension of a Dirham as tahir (in case of blood only). The shafi'is based the small amount on what is known as such by habit العُرف this would apply to pus too in the maliki school.
The above is a summary of the quotes from the fatwa islamweb #18639 on blood and this one on pus #156431 -both in Arabic-(I didn't quote the hanbali opinion so far as I found an English quote). More details on the opinions on pus can be found in the fatwa islamweb #128250 -in Arabic-.
Here a quote from hanbali book:
It says in al-Mughni (1/409):
If he prays and there is some impurity on his garment, even if it is a little, he should repeat his prayer, unless it is a small amount of blood or pus, that one would not think of as anything significant. (Source islamqa #163819)
all these verdicts are based on ahadith such as:
One of us would have a shirt in which she would menstruate and in it she became sexually defiled. Then if she ever saw any drop of blood in it, she would rub it off by applying her saliva. (See for example in Sunan abi Dawod)
So if the amount of blood pus on your clothes was small your prayers were valid else not.
Note that if blood or pus came out of one of the two usual body "outputs" it is certainly invalidating wudu' by all four madhhabs. Else there's a dispute among scholars, but for example islamweb considers the view that it doesn't invalidate the wudu' as stronger.
Refreshing wudu' nevertheless is recommended and one could say required, when you intend to pray as you would stay in front of your Creator and should stand in front of him in the best and cleanest manner.
In this fatwa on islamqa #243145 the dimension of this Dirham is discussed and it diameter is approximately 3 cm (In fact it was compared to silver Riyal coin minted during the reign of the saudi King Abdul Aziz, which had a diameter of 37mm).