It actually does reduce swelling. Here is one of several Medline abstracts. Paracetamol is just another name for Tylenol.
Tidsskr Nor Laegeforen 1993 Feb 10;113(4):439-43
[Anti-inflammatory agents in acute tissue trauma. Choice and effects]
Skjelbred P, Lokken P.
Avdeling for maxillofacial kirurgi, Ulleval sykehus, Oslo.
The choice of drugs to reduce pain and excessive inflammatory reactions after surgery or accidental trauma is reviewed and discussed, with particular reference to a series of Norwegian studies based on bilateral oral surgery. In this model, paracetamol has proved capable of reducing post-operative swelling by about 30%, while acetylsalicylic acid (in common analgesic doses) failed to reduce or even tended to increase swelling. Paracetamol is a recommendable alternative for reducing acute post-traumatic pain and swelling, while acetylsalicylic acid should be avoided. Non-steroidal anti-inflammatory drugs which efficiently reduce rheumatoid swelling may provide good pain relief, but the effect on an acute post-operative swelling is less impressive. In the oral surgical model, glucocorticoids reduced post-traumatic swelling by about 50% and provided better or at least as good pain relief as any tested non-steroidal anti-inflammatory drug, including paracetamol. Single dose or short-term administration of a glucocorticoid is recommended as an efficient and valuable means of reducing both pain and excessive inflammation in surgery and traumatology. Of practical implication in traumatology is the finding that, for both paracetamol and glucocorticoids, almost the same reductions were recorded in swelling and pain whether the drug was administered prior to surgery or 2-3 hours afterwards.
Also, here is the abstract for the other study I mentioned above:
J Clin Endocrinol Metab 2001 Oct;86(10):5067-70
Skeletal muscle PGF(2)(alpha) and PGE(2) in response to eccentric resistance exercise: influence of ibuprofen acetaminophen.
Trappe TA, Fluckey JD, White F, Lambert CP, Evans WJ.
Nutrition, Metabolism, and Exercise Laboratory, Donald W. Reynolds Center on Aging, University of Arkansas for Medical Sciences, 4301 West Markham, Little Rock, AR 72205, USA.
[email protected]
PGs have been shown to modulate skeletal muscle protein metabolism as well as inflammation and pain. In nonskeletal muscle tissues, the over the counter analgesic drugs ibuprofen and acetaminophen function through suppression of PG synthesis. We previously reported that ibuprofen and acetaminophen inhibit the normal increase in skeletal muscle protein synthesis after high intensity eccentric resistance exercise. The current study examined skeletal muscle PG levels in the same subjects to further investigate the mechanisms of action of these drugs in exercised skeletal muscle. Twenty-four males (25 +/- 3 yr) were assigned to 3 groups that received the maximal over the counter dose of ibuprofen (1200 mg/d), acetaminophen (4000 mg/d), or a placebo after 10-14 sets of 10 eccentric repetitions at 120% of concentric 1 repetition maximum using the knee extensors. Preexercise and 24 h postexercise biopsies of the vastus lateralis revealed that the exercise-induced change in PGF(2alpha) in the placebo group (77%) was significantly different (P < 0.05) from those in the ibuprofen (-1%) and acetaminophen (-14%) groups. However, the exercise-induced change in PGE(2) in the placebo group (64%) was only significantly different (P < 0.05) from that in the acetaminophen group (-16%). The exercise-induced changes in PGF(2alpha) and PGE(2) were not different between the ibuprofen and acetaminophen groups. These results suggest that ibuprofen and acetaminophen have a comparable effect on suppressing the normal increase in PGF(2alpha) in human skeletal muscle after eccentric resistance exercise, which may profoundly influence the anabolic response of muscle to this form of exercise.