I also have some small New Year’s resolutions, but I am afraid of pursuing too many goals, and I don’t want to put too much pressure on meyself. I also have some small New Year’s resolutions, but I am afraid of pursuing too many goals, and I don’t want to put too much pressure on myself.

There are very few cases where "don't want ... too much X" happens without the too. My suggestion: unless you specifically know you want to remove the "too" and have a reason, then always use "too much". It is technically correct, and the differences are nuanced, but your sentence feels very unnatural. Also, the reflexive (i.e. I see myself in the mirror) pronoun is "myself". Again, I believe technically your sentence is likely not wrong since you can use "me" as the object, but you will never hear someone saying "I don't want to pout too much pressure on me".